Wikipedia:Articles for deletion/Stereotype space


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was redirect Stereotype space to Reflexive space, Stereotype algebra to Topological algebra, and Stereotype group algebra to Group algebra of a locally compact group. I leave it to the editors of these individual articles to make any adjustments needed to suit these incoming redirects. BD2412 T 17:44, 23 April 2020 (UTC)

Stereotype space

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I cannot find enough literature to establish the notability of this notion. Googling with ""stereotype space" -Akbarov" yields essentially no work on this notion. There is which has an entry on "stereotype space" but the source of this book seems to be the Wikipedia article topological vector space. *Mathematically*, the notion looks interesting and so it should be ok to have some discussion of this notion elsewhere in Wikipedia if the sources can be acquired, perhaps without the term "stereotype space". Another option is to move the article to nlab where the notability requirement is less stringent. -- Taku (talk) 11:47, 8 April 2020 (UTC)


 * The reference to the article by Aristov is given in the list of references:


 * The author uses the term "stereotype algebra" at page 1061. The other sources either use this term, or the term "stereotype space", or mention research in this area. What is the problem? Eozhik (talk) 12:00, 8 April 2020 (UTC)
 * We need non-primary references; i.e., some significant discussion of the notion in papers or books by authors other than the person who introduced the notion. Without them, we cannot say the notion has an established place in the math literature. -- Taku (talk) 12:07, 8 April 2020 (UTC)
 * , what do you call "non-primary references"? As far as I understand, they are not the same as secondary sources. What is the difference? Eozhik (talk) 12:23, 8 April 2020 (UTC)
 * By non-primary, I mean secondary or tertiary sources; works on stereotype space other than you or textbooks. —- Taku (talk) 12:59, 8 April 2020 (UTC)
 * , as I told  at the talk page, there are several secondary sources, including the ones that use the word "stereotype", and the ones that don't. Formally, there is even a tertiary source, a textbook that mentions this research. All these sources are listed in this article, so there is no necessity to google them. That is why your claim "I cannot find enough literature to establish the notability of this notion."— sounds very strange. As well as your interpretation of the Wikipedia rules. Eozhik (talk) 13:24, 8 April 2020 (UTC)
 * No, what we need is to see works on stereotype space by authors other than you. Some sources that mention the work isn’t enough; those sources need to study stereotype spaces with the explicit term “stereotype space”. The notability in Wikipedia is more than whether the term is known; we need to see an established literate on the notion. —- Taku (talk) 13:29, 8 April 2020 (UTC)
 * One way to establish the notability: is there any significant result on stereotype spaces by authors other than you? Has there been a workshop on the topic? We need to see the evidence of research activity by a group of mathematicians not just math works by you. —- Taku (talk) 13:34, 8 April 2020 (UTC)
 * One way to establish the notability: is there any significant result on stereotype spaces by authors other than you? Has there been a workshop on the topic? We need to see the evidence of research activity by a group of mathematicians not just math works by you. —- Taku (talk) 13:34, 8 April 2020 (UTC)

, from what you write I deduce that you don't read the sources. I foresee that the example of my co-author, Evgenii Shavgulidze, who studies the properties of the stereotype spaces together with me — will not persuade you. On the other hand, as we understood, Oleg Aristov, who developed my results on holomorphic duality by studying the stereotype algebra $${\mathcal O}_{exp}(G)$$ of holomorphic functions of exponential type — is not interesting for you, because google doesn't suggest you this reading. What about Yulia Kuznetsova, who proved important continuous version of Pontryagin duality for Moore groups — will this example be suitable? (The term "stereotype space" is contained in the list of keywords of her article.) Or maybe people from Spain and from USA, who study this class of spaces (with another name, but with mentionings of the term "stereotype") — ? Eozhik (talk) 14:13, 8 April 2020 (UTC)
 * Again the problem is that those sources only mention “stereotype space” more specifically your works (but are not about stereotype spaces per se). The question on the notability is not whether people study a class of spaces like stereotype space. The question is whether “stereotype space” itself is notable on its own, *independent of your works*. —- Taku (talk) 14:31, 8 April 2020 (UTC)


 * , what should I think about this: "those sources only mention “stereotype space”"? In these works stereotype spaces are not just mentioned, they are studied. And what about this "The question on the notability is not whether people study a class of spaces like stereotype space. The question is whether “stereotype space” itself is notable on its own, *independent of your works*."? The authors study these spaces not because of "its own", but because they play important role in solving another problem, the propblem of constructing duality theory for noncommutative groups. Which exists independently on my works. Eozhik (talk) 14:44, 8 April 2020 (UTC)
 * And people do not only study these spaces, they suggest concrete solutions of this problem for different classes of groups. Eozhik (talk) 14:47, 8 April 2020 (UTC)
 * The key point is what you said “the propblem of constructing duality theory for noncommutative groups”. That’s what those papers are concerned about. That’s why a stereotype space is not independently notable. What is notable is the problems of duality and how to solve them. It does not follow that one particular solution is notable on its own. Wikipedia is not a place to present a solution (unless that solution becomes notable on its own). —- Taku (talk) 14:55, 8 April 2020 (UTC)
 * What is meant here: "The key point is what you said “the propblem of constructing duality theory for noncommutative groups”. That’s what those papers are concerned about. That’s why a stereotype space is not independently notable. What is notable is the problems of duality and how to solve them."? This needs a translation. Which "problems of duality" do you mean here, ? Eozhik (talk) 15:06, 8 April 2020 (UTC)
 * I have meant problems of constructing good duality theory (for groups or others). That’s a certainly notable problem in mathematics. —- Taku (talk) 15:08, 8 April 2020 (UTC)
 * if that is what you want to see, "I have meant problems of constructing good duality theory (for groups or others). That’s a certainly notable problem in mathematics."— then your reproach becomes even more vague. Because the theory of stereotype spaces suggests a solution of this problem. On the other hand it becomes unclear which nuances do you see between what you say now and what you told before: "The key point is what you said “the propblem of constructing duality theory for noncommutative groups”. That’s what those papers are concerned about. That’s why a stereotype space is not independently notable. What is notable is the problems of duality and how to solve them."? If you say that a duality theory "for groups or others" will be notable, then why aren't the stereotype dualities for them notable? Eozhik (talk) 15:23, 8 April 2020 (UTC)
 * And where do you take these criteria of notability? Eozhik (talk) 15:26, 8 April 2020 (UTC)
 * The notability is not inherited; it is possible that some problem is notable while a solution to it is not necessary notable. The sources provided only show that there is a sufficient math literature on the problem of constructing duality theories that extends the Pontryagin duality (thus the problem is notable). They do not establish the notability for stereotype spaces since, aside from your papers, the primary sources, the secondary sources do not give an in-depth treatment of stereotype spaces. Some of theori results may be interpreted in the language of stereotype spaces but that does not make the theory of stereotype spaces notable on its own. —- Taku (talk) 12:16, 9 April 2020 (UTC)
 * that is not enough. You should present a very sophisticated logical construction to persuade the interlocutor that the results published in peer-reviewed scientific journals are not notable. I would suggest you to send protests to the editorial boards, and after receiving responses to publish them here. And you should find a rule in Wikipedia, that allows you to delete this article. Eozhik (talk) 15:09, 9 April 2020 (UTC)
 * Just because something appeared in a math journal doesn’t make it notable from the view of Wikipedia. That something has to have a strong presence in math literature; i.e, there is a sizable group of researchers studying it for an extended time period. Just like not every single actor who had a role in a movie is notable enough for a Wikipedia article. —- Taku (talk) 10:55, 10 April 2020 (UTC)

Until now, I have not seen anyone here except the initiator of this discussion. And I want to say a few words to those who have not yet formed their opinions.

In what I saw here, the main thing for me is this statement by :
 * , so your point is that a Wikipedia article must describe only what is written in textbooks, right? Eozhik (talk) 12:04, 8 April 2020 (UTC)
 * Yes. Textbooks or some major monographs... -- Taku (talk) 12:11, 8 April 2020 (UTC)

I have not yet found confirmation of this thesis. The links that gave to me don't contain it. I will listen with interest to the (promised) opinions of people about this, but no matter what I hear, I want to notice that what is happening is not called honesty:

1. If this important rule is really accepted in Wikipedia, it should be clearly spelled out in the local laws so that situations are not provoked when a person, not knowing about anything like this, spends time writing an article, editing it, searching for sources and the rest, and suddenly discovers that all his work has been thrown into the bin. This is a very important rule, fundamental to such resources, and if it really works here, then the situation when somebody refers to it, despite the fact that it is not written anywhere, is called a dishonesty.

2. On the contrary, if this rule is not accepted on Wikipedia (which is logical to think when it is not visible anywhere), then a reference to it looks like a cheating.

Ladies and gentlemen, you should deal with your laws, because this situation is a disorder. Eozhik (talk) 15:43, 9 April 2020 (UTC)


 * Note: This discussion has been included in the list of Mathematics-related deletion discussions. Coolabahapple (talk) 22:25, 9 April 2020 (UTC)


 * Keep-the concept is cited in this paper:. I think the concern was that the author of the papers was a crackpot or crank. If this concern was true, you wouldn't see a paper of his being cited by others in reputable literature.--Epiphyllumlover (talk) 23:00, 9 April 2020 (UTC)
 * That one of the main references has been cited once by a different paper, which itself has only ever been cited once (by its own author), is not a very strong reason to keep a WP article. — MarkH21talk 20:12, 15 April 2020 (UTC)
 * I agree with here. XOR&#39;easter (talk) 20:15, 15 April 2020 (UTC)


 * That's where we came now. Gentlemen, if this is what was meant, then the investigation procedure in such cases needs a formalization. Now it looks awfully. My habilitation thesis was devoted to this topic. It was at the Moscow State University, Faculty of Mechanics and Mathematics. The reviewers were from the Moscow State University, from the Steklov Institute of Mathematics and from the University of Caen Normandy. Eozhik (talk) 07:38, 10 April 2020 (UTC)


 * No, that’s not the nomination reason; I am not saying what he does isn’t a valid mathematics research. But that’s not enough to satisfy the notability requirement. To quote from Notability “If a topic has received significant coverage in reliable sources that are independent of the subject, it is presumed to be suitable for a stand-alone article or list.” All we have is the significant works on the stereotype spaces by User:Eozhik, Sergei Akbarov, himself. We need works by other than him on stereotype spaces with the explicit term “stereotype spaces“ (for example, the abstract of the paper by Aristov uses the term “locally convex algebra” and no “stereotype” in the abstract). As far as we understand, there is no such works. For the notion to be notable, at minimum, we need to know other researches use the term ”stereotype space” in their own works independent of User:Eozhik. —- Taku (talk) 10:41, 10 April 2020 (UTC)


 * , this"We need works by other than him on stereotype spaces with the explicit term “stereotype spaces“ (for example, the abstract of the paper by Aristov uses the term “locally convex algebra” and no “stereotype” in the abstract). As far as we understand, there is no such works."— is solipsism. Let us bet? If I find an article (in a peer-reviewed journal) where the author (other than me) explicitely uses the term "stereotype space" or "stereotype algebra", you pay me, say, $ 100. If not, I pay you this amount. Agree? Eozhik (talk) 11:54, 10 April 2020 (UTC)
 * I forgot to add: this will be a work in the list of references of the discussed article. Eozhik (talk) 12:01, 10 April 2020 (UTC)


 * More precisely, I should have said: we have not been presented a paper that (1) does not have you as an author or a co-author and that (2) explicitly states that it studies stereotype space; e.g., it has the term "stereotype space" in title or in abstracts. To repeat, what we need is an evidence that there is a sizable group of researches who study stereotype spaces *per se* for an extended period of time. The papers by authors other than you that are cited in the article are, as far as I can tell, about duality theory. They *only* establish the notability of the problem of duality but not of stereotype spaces per se. -- Taku (talk) 12:24, 10 April 2020 (UTC)


 * , the problem with you is that you do not want to be responsible for your words. What about the bet? Eozhik (talk) 12:40, 10 April 2020 (UTC)
 * I don't need to bet or supply the evidence of absence. All I'm saying is there is the absence of evidence that stereotype space is something widely studied in the math community. Without such evidence, we cannot have the article. -- Taku (talk) 13:38, 10 April 2020 (UTC)
 * When a person is ready to be responsible for his words, there is no problem for him to bet. See how frivolous you are? Eozhik (talk) 13:52, 10 April 2020 (UTC)

And another problem is that all the way you change the requirements and/or come back to old ones. Initially you claimed that there must be papers with the title that includes the term “stereotype space”"What we need is a reference that discusses stereotype spaces *in depth* by authors other than you. Is there any? E.g., some paper whose title includes the term “stereotype space”." When I gave these references, you changed the requirements: We need non-primary references; i.e., some significant discussion of the notion in papers or books by authors other than the person who introduced the notion. Without them, we cannot say the notion has an established place in the math literature. -- Taku (talk) 12:07, 8 April 2020 (UTC) TakuyaMurata, what do you call "non-primary references"? As far as I understand, they are not the same as secondary sources. What is the difference? Eozhik (talk) 12:23, 8 April 2020 (UTC) By non-primary, I mean secondary or tertiary sources; works on stereotype space other than you or textbooks. —- Taku (talk) 12:59, 8 April 2020 (UTC) When I pointed out that these references are already given, you changed your claims like this: No, what we need is to see works on stereotype space by authors other than you. Some sources that mention the work isn’t enough; those sources need to study stereotype spaces with the explicit term “stereotype space”. The notability in Wikipedia is more than whether the term is known; we need to see an established literate on the notion. —- Taku (talk) 13:29, 8 April 2020 (UTC) One way to establish the notability: is there any significant result on stereotype spaces by authors other than you? Has there been a workshop on the topic? We need to see the evidence of research activity by a group of mathematicians not just math works by you. —- Taku (talk) 13:34, 8 April 2020 (UTC) When I wrote that this is done in the listed papers, you wrote that the research must be "independent of my works": "Again the problem is that those sources only mention “stereotype space” more specifically your works (but are not about stereotype spaces per se). The question on the notability is not whether people study a class of spaces like stereotype space. The question is whether “stereotype space” itself is notable on its own, *independent of your works*. —- Taku (talk) 14:31, 8 April 2020 (UTC)" When I wrote that it is, you wrote that these works must be focused on a "notable problem in mathematics": "I have meant problems of constructing good duality theory (for groups or others). That’s a certainly notable problem in mathematics. —- Taku (talk) 15:08, 8 April 2020 (UTC)" When I wrote that they study exactly the problem that you declare notable, you forgot everything and today you write that there must be papers with the explicit term “stereotype spaces“"We need works by other than him on stereotype spaces with the explicit term “stereotype spaces“ (for example, the abstract of the paper by Aristov [4] uses the term “locally convex algebra” and no “stereotype” in the abstract). As far as we understand, there is no such works."So this brought us back to the beginning. When I suggested to bet, you changed your claims like this:"(1) does not have you as an author or a co-author and that (2) explicitly states that it studies stereotype space; e.g., it has the term 'stereotype space' in title or in abstracts."Since no one of these requirements is mentioned in the rules of Wikipedia, I would say, there is a big problem here. Eozhik (talk) 13:54, 10 April 2020 (UTC) Would anybody help me to name this problem? Eozhik (talk) 14:05, 10 April 2020 (UTC)


 * I admit I was vague about what type of references I am asking for. In fact, I don’t really care about the types of references. Any reference will do if it establishes the notability of stereotype spaces. What I have been doing is explaining why the references you provide fail to establish the notability from the view of Wikipedia, and the notability is a requirement: I have already quoted Notability. —- Taku (talk) 15:21, 10 April 2020 (UTC)
 * To clarify, Taku, do you accept the citation I linked to in my previous post? If one were to find two more of a similar nature that would count in your opinion as meeting GNG?--Epiphyllumlover (talk) 23:57, 10 April 2020 (UTC)
 * In my opinion, those references do not do; as far as I can tell, those non-primary sources only refer to or use the works of User:Eozhik. So, we know his research works are legitimate but it does not mean his work is notable in the Wikipedia sense. Anyone can publish a paper introducing a new concept and if the work is good gets a citation. That does not mean we can have a Wikipedia article on topic. we need evidence that this topic is something studied by a sizable group of researchers; e.g.. as I said, the simplest evidence of this would be any paper other than User:Eozhik that uses the term “stereotype space” in title or abstract. (By the way, I don’t think GNG covers a math topic; so the part of difficulty is a lack of the guidelines.) —- Taku (talk) 09:07, 11 April 2020 (UTC)
 * Again this is my interpretation of the notability requirement but for a math topic to be covered in Wikipedia, we need to see some evidence of significance. In Wikipedia, we cannot have an article on every single actor or every single album just because they are legitimate actors or albums. Likewise, for a math topic, we need some evidence of significance; which can be in any form; e.g., there are a number of papers denoted to the topic, there has been a workshop devoted to the topic, chapters in a textbook on the topic, etc. —- Taku (talk) 09:23, 11 April 2020 (UTC)


 * As I see, now it’s not enough for other authors to use this term, it’s not enough for them to prove statements in which this term is used, it is not enough for these statements to solve significant problems of mathematics. Now it is necessary for this term to be directly mentioned in the title or in the abstract of the articles that don't belong to me. The rest does not count. The content of the papers, the importance of the results, the usage of the term inside the paper, the keywords, — these details are no longer important.


 * Gentlemen, this continuous moving of the border of requirements looks indecent. Why the border should now lie here, and not a few centimeters to the left or to the right — is a mystery, and the end of this is not seen. And this style of accusations in itself poses a certain moral problem:"“I don’t understand what is written here, but it doesn’t matter, because for me it’s customary to simply blame the author for various absurd things, and when he makes excuses, his weak point is usually revealed, and this allows me to declare him a loser. And there is no discomfort in the fact that my accusations are absurd and self-contradictory because the goal is more important than the form: even if the weaknesses are not revealed, he will lose because I set the rules of the duel and I can change them as I want.”"


 * So I want to ask, is there a person here who could formulate the claims without deception? It would be fine if he could demonstrate responsibility for his words and have an idea of the encyclopedic traditions and the boundaries of the rational. Eozhik (talk) 12:59, 11 April 2020 (UTC)
 * Taku, I have similar reservations about the use of the "General Notability" guidelines with respect to not only math, but also niche scientific topics. The basic problem is that WP already skews towards what might be called "pop sci" type science coverage. Ostensibly the GNG requirement will help us keep out the cranks and crackpots-- but unfortunately the sensation they generate often makes them notable enough for an article, though it be critical of their theories. As a result I think it would be best to use a stricter interpretation of GNG against anything that is considered crank / crackpot territory outside of WP. For scientific and mathematical concepts not associated with cranks / crackpots, being cited or employed by three different authors in peer-reviewed journals should be enough to meet GNG.--Epiphyllumlover (talk) 21:17, 11 April 2020 (UTC)
 * I have never had a crank / crackpot concern; I am 100% certain that his work is a legitimate mathematical research. The question here is how much mathematical research topics Wikipedia should cover as standalone articles and the GNG is quite irrelevant to such a question. My view is that for a math topic to be covered, it needs to be more than one person's work (with some exception, like when the work is cited hundreds times); i.e., it's something studied by a math community. We have not been presented evidence of that. Here is an AfD quite similar to this one Articles for deletion/Word-representable graph; legitimacy is often not enough. In any case, I think my position is clear; now, we really need opinions from other editors (in addition to yours). -- Taku (talk) 22:17, 11 April 2020 (UTC)
 * So it has to be cited hundreds of times instead of three? Few people get their papers cited that much, especially in math. We don't treat animal and plant species with this! It only needs to be an accepted name by the scientific community. Why can't we treat math concepts like we do organisms?--Epiphyllumlover (talk) 04:50, 12 April 2020 (UTC)
 * No, no, I was taking about an exception. My point was that a math research topic needs to be more than one person's work to be covered in Wikipedia; it needs to be studied by a sufficiently large group of mathematicians. Again the simplest evidence of such would be; there has been some workshop on the topic or a discussion on the topic in a textbook. Also, I do not believe the "stereotype space" is an "accepted name by the scientific community"; because often in abstracts or titles, you see terms like locally convex algebra and such, instead of "stereotype space". Presumably this is because "stereotype space" is not a commonly understood term. In mathematics, anyone can publish a paper introducing a new name and it might get cited; that does not mean that new name is commonly accepted. Workshops, textbooks, monographs, etc. are needed to determine some concept is now firmly part of the mathematical canon (cf. WP:NEOLOGISM) Also, again please take a look at Articles for deletion/Word-representable graph; in this case, we do have a paper on the subject other than the originator of the topic and there is an (upcoming) textbook on the topic. So in that case, we do have evidence of significance of the topic. For "stereotype space" to be notable from the view of Wikipedia, we also need to see a similar kind of evidence. -- Taku (talk) 11:36, 12 April 2020 (UTC)

no, there are no special standards for mathematics. Everything is the same everywhere. As I wrote here, in the Soviet Mathematical Encyclopedia of 1977-1985 there are many articles without references to textbooks. It was translated later in Springer and is available now under the name “Encyclopedia of Mathematics”. The (random) examples are the following:

Condensing operator

Fano surface

Fréchet surface

Fubini theorem

Fourier indices of an almost-periodic function

Heegaard decomposition

Homeomorphism group

Hypercomplex functions

Suzuki 2-group

Superharmonic function

Tertiary ideal

All these requirements about textbooks, terms in titles, in annotations, etc. are exclusively figments of the imagination of our interlocutor. They neither follow from the local rules of Wikipedia, nor from the encyclopedic traditions. Eozhik (talk) 14:31, 12 April 2020 (UTC)
 * Taku, could you provide us list of either synonyms or broader and inclusive terms and phrases for stereotype space? "locally convex algebra" is one. After you do this, Eozhik, I think it would be good to evaluate them and whether you agree with Taku's judgement.--Epiphyllumlover (talk) 17:33, 12 April 2020 (UTC)
 * I don’t think there are many synonyms for stereotype spaces (locally convex algebra isn’t a synonym but a related term); they are a special case of a topological vector space. So, it’s fine to mention the term “stereotype space” in that article. But the question here is whether there are enough literature on the subject to justify a standalone article in Wikipedia; by literature, I mean the works other than by Eozhik. His works are indeed extensive but we need works by other people so that we know the topic is something studied by a math community not by an individual. —- Taku (talk) 20:29, 13 April 2020 (UTC)


 * in fact, this term has synonyms. Probably, the most authoritative source is the book by G. Köthe, "Topological Vector Spaces", Vol. I, where these spaces are called “polar reflexive spaces” (§ 23.9, p.308). Apparently, I should have mentioned this in the article, but I forgot about it because, according to my observations, mathematicians did not form a general opinion as to which term is more convenient, some do not use any term at all, and in addition, this class has been opened and reopened many times. M.F.Smith in her pioneering work did not name these spaces in any way, she simply described the topology on the dual space X * and proved that X = X ** (and the topology she introduced was formally different from the topology of uniform convergence on totally bounded sets, but the results on Banach and reflexive spaces follow from her constructions). Same thing with W.C.Waterhouse. B.S.Brudovsky called these spaces "c-reflexive space" (as far as I remember), and K.Brauner calls them “p-reflexive spaces”. F. Garibay Bonales, F.J. Trigos-Arrieta, R. Vera Mendoza, S. Hernandez call them polar-reflexive spaces following Kothe. In Russia, these spaces are usually called "stereotype". Eozhik (talk) 10:36, 14 April 2020 (UTC)
 * Can you list a variety of such Russian sources here?--Epiphyllumlover (talk) 21:25, 14 April 2020 (UTC)
 * , if we don't count my own papers and the papers of my co-author, then the list will be the following:
 * There are also some papers that are not published yet, only announced in arXiv, in particular, this one:
 * Oleg Aristov (2020). On holomorphic reflexivity conditions for complex Lie groups. arXiv:2002.03617
 * In three of these papers the stereotype spaces are not studied "in itself", the authors apply them to an old problem, the problem of constructing duality theory for non-commutative groups. And they receive important and very unexpected results: they construct duality theories for different classes of groups without the shortcomings of the other theories, as it is explained here and here:"One of the drawbacks of these general theories, however, is that in them the objects generalizing the concept of group are not Hopf algebras in the usual algebraic sense. This deficiency can be corrected (for some classes of groups) within the framework of duality theories constructed on the basis of the notion of envelope of topological algebra."Eozhik (talk) 21:58, 14 April 2020 (UTC)
 * There are also some papers that are not published yet, only announced in arXiv, in particular, this one:
 * Oleg Aristov (2020). On holomorphic reflexivity conditions for complex Lie groups. arXiv:2002.03617
 * In three of these papers the stereotype spaces are not studied "in itself", the authors apply them to an old problem, the problem of constructing duality theory for non-commutative groups. And they receive important and very unexpected results: they construct duality theories for different classes of groups without the shortcomings of the other theories, as it is explained here and here:"One of the drawbacks of these general theories, however, is that in them the objects generalizing the concept of group are not Hopf algebras in the usual algebraic sense. This deficiency can be corrected (for some classes of groups) within the framework of duality theories constructed on the basis of the notion of envelope of topological algebra."Eozhik (talk) 21:58, 14 April 2020 (UTC)


 * I think it is worth noting that this area, topological vector spaces, is currently not as popular as in the 60s and 70s, for this reason now quite a few people are engaged in it. In particular, conferences on this science are not being held now (and that is why there are no workshops). After the well-known events in Russia I know only several people here who are interested in these things. I believe, however, that this doesn't mean that these people must be treated as madmen. Eozhik (talk) 22:17, 14 April 2020 (UTC)
 * In order to demonstrate notability under the GNG rule, you would need to show examples of the use of the term from the papers, and it would probably have to be employed more than once. (And please translate for us, too.) This is because term "stereotype" is not evident from the titles.--Epiphyllumlover (talk) 04:30, 15 April 2020 (UTC)


 * , I don't understand. Does this mean that people don't look inside the articles? I can give pictures if this is necessary.


 * Eozhik (talk) 05:52, 15 April 2020 (UTC)
 * For a pdf, no they probably don't, unless you provide a phrase for them to search. For Google Books, it often highlights the phrase for you which is nice. I've never seen pictures in a deletion discussion before. If they don't get deleted, this is great and I think it will prove your point better than anything you've written so far.--Epiphyllumlover (talk) 06:04, 15 April 2020 (UTC)
 * , what were we talking about all this time, if it turns out that people don't look inside the references that give to each other? If this is important the procedure must be formalized by indicating that the author of the article is obliged to give scanned pictures that confirm references. Eozhik (talk) 06:21, 15 April 2020 (UTC)


 * Delete per nom, and also because "mathematicians did not form a general opinion as to which term is more convenient, some do not use any term at all, and in addition, this class has been opened and reopened many times". This quote by the main opponent to deletion shows clearly that the term "stereotype space" is not notable by itself. The notability of the associated concept (topological space that is isomorphic to its bidual) is less clear. The defining property is evidently interesting for everybody who works on topological spaces. So, Topological vector space could have section on this subject, and all names that have been given to this property could be redirected there. For deserving having its own article, such a concept should either having been studied by many people (this is not the case here), or it should have been useful outside the strict study of the concept. No evidence has been given that this is the case here. Therefore I support deletion . D.Lazard (talk) 18:01, 14 April 2020 (UTC)


 * two questions:"For deserving having its own article, such a concept should either having been studied by many people (this is not the case here)" How many people had to study this class of spaces so that in your opinion it became notable? "or it should have been useful outside the strict study of the concept. No evidence has been given that this is the case here." There is a section in the article devoted to applications. Why don't you count it? Eozhik (talk) 19:38, 14 April 2020 (UTC)
 * D.Lazard, Could you work at adding a section to Topological vector space, even now? In particular, the stereotype space article has more equations than the topological vector space article, and appears to be more developed. Can you bring topological vector space to a similar, or even better level?--Epiphyllumlover (talk) 19:44, 14 April 2020 (UTC)
 * For me, being "useful outside the strict study of the concept" means the use by others than the inventor of the concept, or the solution of a problem that has been set before the invention of the concept. In the section on applications, I see only generalizations and reference to works by the inventor of the concept and his frends, not the solution of pre-existing problems. D.Lazard (talk) 20:17, 14 April 2020 (UTC)
 * constructing duality theories for non-commutative groups is a pre-existing problem. And this problem is far from a final solution. That is why the "inventor and his friends" find support from colleagues abroad (and publish their results in reliable journals). Eozhik (talk) 20:41, 14 April 2020 (UTC)


 * Comment Wikipedia policy WP:PRIMARY say . As this article is based only on primary sources, this is sufficient for deleting it, without examining its notability. D.Lazard (talk) 20:17, 14 April 2020 (UTC)
 * There are secondary sources in the article as well. Eozhik (talk) 20:41, 14 April 2020 (UTC)


 *  Delete Redirect to Reflexive space: Per the arguments made by Taku and D.Lazard, this is not a term widely-used by independent secondary sources to the point that WP:GNG is not met and WP:NEOLOGISM can apply.Once could argue for a merge to topological vector space, the greater class of objects for which there is substantial secondary sources and standard terminology, but very little content in this article should be merged there on the basis of WP:DUE. — MarkH21talk 01:48, 15 April 2020 (UTC); changed to redirect 03:49, 22 April 2020 (UTC)
 * this sounds as if there was a controversy between people who prefer to use the term "stereotype" and those who use other terms. There is no such a controversy: people use differenct terms, and this is normal for mathematics. For example, some people use the term linear mapping while others linear operator, and there are no misunderstandings between them. Similarly people use different notations. Eozhik (talk) 06:44, 15 April 2020 (UTC)
 * I didn't say anything about there being a controversy. There just needs to be evidence that the term is widely used. In the evidence that you provided (currently in image form), I see four total articles that mention the term. But one of them has you as a co-author and one of them only says that Akbarov calls them stereotype spaces. That's not really evidence that many people use the term. For linear mapping and linear operator, we can easily find thousands of different independent sources that use each term. — MarkH21talk 19:27, 15 April 2020 (UTC)
 * , it’s not my fault that Wikipedia has no rule regulating how many references there should be. And it’s not my fault that when I posted this article 7 years ago nobody warned me. This is what I am talking about here. If these details were indicated in the rules, this would save everyone present from unnecessary waste of time. Eozhik (talk) 12:43, 16 April 2020 (UTC)
 * However,, there is still a possibility to edit this article by adding there the term "polar reflexive space" from G.Köthe's book. The relations between these two terms are the same as between linear map and linear operator. This would resolve this local problem, although, of course, the global one (concerning the rules) will remain actual. Eozhik (talk) 13:06, 16 April 2020 (UTC)
 * The notability guidelines are intentionally vague so that we may rely on editor consensus instead of rigid numerical rules. If we had "more than 10 independent secondary sources use the term", for instance, what if there were 9 Annals papers from 9 different renowned mathematicians dedicated to the term and its theory and a Fields Medal awarded to someone for developing its theory? That's very different from 11 papers from two mathematicians publishing in an obscure journal that only briefly mention the term. Having rigid rules would prevent us from properly assessing the merits of a topic and would make WP overly inflexible. — MarkH21talk 13:18, 16 April 2020 (UTC)
 * is exactly correct here. As I wrote below, trying to invent numerical scales and thresholds is likely to create an illusion of precision rather than actual clarity. XOR&#39;easter (talk) 13:31, 16 April 2020 (UTC)
 * And by flexibility you mean the possibility to kill other people's work without any legitimate reason. And to advertise the work of the people that you liked, also without being bothering with formalities. I have an opposite opinion. There must be clear rules that allow people to play fair game independently of whether they are your friends or not, whether they live in Europe, America, Russia etc., whether they have enough money to publish their own journals or not. Those who have these money, have the possibility to advertise themselves without Wikipedia. Eozhik (talk) 13:43, 16 April 2020 (UTC)
 * Please, let's assume a measure of good faith here. Nobody is out to "kill" anything. We're not trying to stop anyone from posting on the arXiv, or publishing in journals, or writing a textbook, or expanding the nLab's entry on stereotype spaces. We're not even objecting to having material about stereotype spaces in another article, like topological vector space. We're just trying to decide, honestly and as fairly as we can, whether having three whole dedicated articles &mdash; stereotype space, stereotype algebra, stereotype group algebra &mdash; is the right course of action. As explained, if the Wikipedia community relied upon numerical rules like "a topic must be mentioned in 10 different journal articles" or "a paper must be cited at least 15 times", then people could just game those rules, just like they already game their impact factor and h-index. Making the rules sound exact does not mean that people will play fair. We rely upon community discussion because we believe that building an encyclopedia is too important for metrics that are only superficially precise. XOR&#39;easter (talk) 15:06, 16 April 2020 (UTC)
 * I spent a lot of time for creating and editing these articles. When doing this I was sure that this is legitimate and nobody will destroy my work. Because this is in human culture that if something does not contradict the laws, it is legitimate. And these articles are important for us since they give us a possibility to explain to our colleagues what we are doing (there are not so many possibilities, you can trust me). Even nLab, although being a very good website, is not so good since there are technical problems with pictures there (as far as I know). You compare this with h-index and impact factor, but the difference is that to play those games people already should have a good support from their countries: the possibilities to publish their own journals, to visit conferences, etc. for being successful. A mathematician living in Russia, or in Georgia, or in Uzbekistan is not in the same conditions as the one who lives in USA (and who because of this can easily enter the necessary clubs). Of course, nobody of us will refuse to use arXiv or to publish our works in normal journals after this story. But what happens here is not fair. And this contadicts human understanding of decency. Even h-index and impact factor are more fair, since they are based on clear rules. Eozhik (talk) 15:56, 16 April 2020 (UTC)
 * I am not against merging this with other articles like topological vector space and topological algebra (although I foresee problems since these articles are only drafts). Another possibility, as I told already, is to add the term "polar reflexive" to the article with the references to Köthe and other authors. But what I definitely don't like is the idea to kill everything. On the base of suspicions. Eozhik (talk) 16:38, 16 April 2020 (UTC)
 * It's naturally disappointing if something that you have worked on is nominated for deletion, but the general notability guideline has always been clear (including in 2012) that the most basic metric is significant coverage in reliable sources that are independent of the subject. There's not really much of that in this case, with perhaps one(?) example in the Kuznetsova article. If there is a lot of coverage from Russian, Georgian, or Uzbek mathematicians (or journals), the outcome is the same as if the coverage is from American mathematicians; there's no difference here. The article deletion discussions on WP are quite fair and based on logical arguments. — MarkH21talk 16:36, 16 April 2020 (UTC)
 * formally these requiremets are met. "More than a trivial mention", "reliable", "secondary sources", "independent of the subject", the only vague point is "presumed". The rules must be more clear. And your idea of "flexibility" is not convincing. Eozhik (talk) 16:55, 16 April 2020 (UTC)
 * I see only one reference (Kuznetsova) that can be considered significant coverage and independent, not multiple. Also, this "flexibility" isn't my idea; the guidelines were agreed upon via the consensus of many many WP editors over many years. — MarkH21talk 17:15, 16 April 2020 (UTC)
 * what are you looking for? These spaces are studied by different authors. Some of them, like Smith, don't use any terms at all, some, like Brauner, use the term "p-reflexive", some, like Garibay Bonales, Trigos-Arrieta, Vera Mendoza, Hernandez, write "polar reflexive", some, like me, Kuznetsova, Aristov, Shavgulidze, use the term "stereotype". Some study algebras (stereotype or topological). There are mutual references. Are you speaking about generalizations of my own results? They are in the works by Aristov, Kuznetsova and Shavgulidze. Eozhik (talk) 17:54, 16 April 2020 (UTC)
 * For multiple published papers not written by you or your co-authors that explicitly use the term stereotype ____ in-depth (i.e. not just Akbarov calls them "stereotype ____"). — MarkH21talk 21:57, 16 April 2020 (UTC)
 * Stylistically it would be good to add here: "...and not by people who are familiar with you". this is the situation when mathematicians in different countries use different terms. This often happens, I told this already when I gave the example of linear mapping and linear operator. As far as I understand, adding to the article another, equivalent term, "polar reflexive space", will not satisfy you, right? Eozhik (talk) 22:10, 16 April 2020 (UTC)
 * Perhaps merging this to Topological vector space or Reflexive space is more appropriate, although I see that the latter already has a section on this. I'm not sure whether "stereotype space" and "polar reflexive space" are collectively notable enough for an article, although even in that case one must determine a title based on WP:COMMONNAME, but that's a separate issue. — MarkH21talk 07:57, 18 April 2020 (UTC)

 Relisted to generate a more thorough discussion and clearer consensus. Relisting comment: I'm not reading walls of text. Please give concise, policy-based reasons to delete or keep. The images added here look like copyvios; I've reported them at Commons.

Please add new comments below this notice. Thanks,  Sandstein   06:34, 15 April 2020 (UTC)
 * I don't understand what happens and what to do with these pictures. Eozhik (talk) 06:44, 15 April 2020 (UTC)
 * I agree with that, except for really involved people, nobody want to read these walls of texts. Therefore, I have collapsed the long technical discussion that follows the nomination and does not contain clear policy-based arguments. Remains uncollapsed the nomination, the comments and !votes that are opened by a bolface header, and their answers.
 * In summary, so far, three editors support deletion, (the nominator),  and  (myself). Two editors are for keeping the article,  and, the latter having a blatant WP:COI, being the author of the WP article and the author of its main references. D.Lazard (talk) 09:08, 15 April 2020 (UTC)


 * , explained his motives to me differently, not like you:"except for really involved people, nobody want to read these walls of texts" For me the rules of this game remain unclear, what I find very strange. In particular, you did not comment this: "How many people had to study this class of spaces so that in your opinion it became notable?" Eozhik (talk) 09:41, 15 April 2020 (UTC)
 * Sandstein's comment is about the upload of copyrighted images. "Walls of text" is about the whole discussion that I have collapsed. By the way, this page is not for personal discussions between editors. So, I do not answer here to any personal question. D.Lazard (talk) 10:38, 15 April 2020 (UTC)


 * , this is not a personal question, this concerns the rules of Wikipedia. If you write that your vote is based on this opinion"For deserving having its own article, such a concept should either having been studied by many people (this is not the case here)"— while there is no rule that establishes the standards, it is natural that interlocutor asks you where you find these standards. Eozhik (talk) 13:30, 15 April 2020 (UTC)


 * Delete The topic seems to lack notability in independent sources such as the Encyclopedia of Mathematics. Andrew🐉(talk) 10:04, 15 April 2020 (UTC)
 * Andrew, Eozhik noted that the term "stereotype" is used by Russians more. I am hoping he will share some of these foreign journals with us and translate it for us. It is possible that differences in terminology between the Encyclopedia of Mathematics and Eozhik could be due to language.--Epiphyllumlover (talk) 16:52, 15 April 2020 (UTC)
 * Could be. But it is true that we cannot find a general reference work that gives the definition of a stereotype space. Of course, Google can miss some references, especially off-lines but so far we are not presented evidence that the notion has gained a general currency in the mathematics community. —- Taku (talk) 19:26, 15 April 2020 (UTC)
 * This is not true. actually, all Russian mathematical journals (at least important ones) are translated into English, so there is no necessity to translate anything (thank god). Moreover, almost all recent papers are translated now by the authors and posted in arxiv.org. Most of the articles I refered to as well. That is why I have doubts that still (after removal those pictures) there is a necessity to give the quotations. As  said,"I expect the people who participate in a deletion debate for a fairly abstruse mathematical topic to be conscientous and check into the available sources, even if it requires clicking a mouse button to expand a section of text." (He meant clicking this Wikipedia page, but the difference is not too great, I believe.) The absense of this term in Encyclopedia of Mathematics is explained by the fact that after collapse of the Soviet Union (I am not its fan, but the problem exists) mathematics and mathematicians are not well-payed, and there is not enough money for publishing many mathematical books, including encyclopedias. Eozhik (talk) 12:23, 16 April 2020 (UTC)

what does this mean:
 * "Note: This discussion has been included in the list of Mathematics-related deletion discussions. Coolabahapple (talk) 22:25, 9 April 2020 (UTC)"

Eozhik (talk) 14:05, 15 April 2020 (UTC)
 * The Wikipedia community maintains lists of ongoing deletion debates organized by topic. Mathematics is one such topic; there are many others. These lists help editors who have an interest in a subject area to stay informed about when articles pertaining to that subject have been nominated for deletion. For example, I myself make fairly regular checks on the lists for mathematics, science, and biographies of scholars and academics. XOR&#39;easter (talk) 15:59, 15 April 2020 (UTC)
 * thanks for your response to 's question, my attitude is the more wikieditors involved in afds the better, hence why i add them to these lists:) Coolabahapple (talk) 16:30, 15 April 2020 (UTC)

(Further) comment. Fondamentally, this article is about duality in topological vector spaces. There are a Groethendieck's master work and a Bourbaki's book on topological vector spaces. I have not read them, but I do not imagine that they do not study duality, since duality was fundamental for both authors. None is mentioned in this article, even in the history section. I suspect that many of the theorems that appear in the article can be found in these works, although they are all presented as found by Akbarov. Whether I am wrong or not is not important, as, in any case, the article is biased as not giving any indication of what is really new in Akbarov theory, and what has been discovered by previous authors. This makes the article purely self-promotional. D.Lazard (talk) 13:36, 16 April 2020 (UTC)
 * Comment--the best evidence of notability (that is, the list of citations and the images) is now collapsed. This risks rendering the whole deletion discussion illegitimate and I expect that it could be overturned should Eozhik wish to pursue deletion review.--Epiphyllumlover (talk) 16:52, 15 April 2020 (UTC)
 * should just post quotes and links, not copyvio images. The removal of copyvio images isn’t a reason for DRV. — MarkH21talk 17:09, 15 April 2020 (UTC)
 * The images are significantly worse for discussion purposes than simple quotations of text, not least because it's harder to tell how many of them come from the same source. XOR&#39;easter (talk) 18:21, 15 April 2020 (UTC)
 * Everybody can read the collapsed part of the discussion by clicking on the button "show" on the right. D.Lazard (talk) 17:28, 15 April 2020 (UTC)
 * Pretty sure you wouldn't like it if someone collapsed your best arguments. (But they tend not to read it and that is the point of collapsing.) And (directed to XOR&#39;easter), the citations were collapsed too. Is the purpose of inexperience with the methods of this website to give a tactical advantage to an opposer? Or is it to learn? Do you expect the closer to enable this sort of thing?--Epiphyllumlover (talk) 19:48, 15 April 2020 (UTC)
 * I expect the people who participate in a deletion debate for a fairly abstruse mathematical topic to be conscientous and check into the available sources, even if it requires clicking a mouse button to expand a section of text. And I expect those people to organize their thoughts sufficiently well that they can articulate a reason to keep or delete the article that is grounded in Wikipedia's policies and guidelines, providing an honest evaluation in terms that someone who does not specialize in the mathematics can still understand. I expect that mathematicians and scientists can do what I do and recognize that not every idea I have thought up and published necessarily belongs in an encyclopedia yet. I expect that scholars can appreciate how evaluating research work can be difficult, and that trying to invent numerical scales and thresholds is likely to create an illusion of precision rather than actual clarity. I expect that intellectuals can summon the emotional maturity not to treat a discussion about how to organize an encyclopedia like it is a battlefield. XOR&#39;easter (talk) 20:04, 15 April 2020 (UTC)
 * Sorry, the only statement I intended to direct you specifically was that the citations were collapsed too.--Epiphyllumlover (talk) 20:32, 15 April 2020 (UTC)
 * Correct me if I am wrong, but no non-primary sources that are not already listed at stereotype spaces are presented at this discussion so far. So no key sources are hidden. —- Taku (talk) 21:24, 15 April 2020 (UTC)
 * To find them go to "Technical discussion continued" and uncollapse it. The relevant part of the discussion can be found by doing a browser search for " Kuznetsova "--also see the screenshots slightly below the Kuznetsova and other citations.--Epiphyllumlover (talk) 00:45, 16 April 2020 (UTC)
 * I think the key phrase was not already listed at stereotype spaces. The Kuznetsova and Hernández–Trigos-Arrieta sources are both referenced in the article already. The assumption is that anyone looking at this AfD would look at the reference list. — MarkH21talk 01:47, 16 April 2020 (UTC)


 * This is the most impressive sentence: "Whether I am wrong or not is not important" It's not enough to suspect, :"I suspect that many of the theorems that appear in the article can be found in these works, although they are all presented as found by Akbarov." In such cases, it is considered necessary to provide evidence. And you can send protest to the journals where this is published. Eozhik (talk) 13:58, 16 April 2020 (UTC)
 * Was the term in use during the soviet era? Do you have any of these soviet era offline works laying around? If so, please cite them for us and give short quotes.--Epiphyllumlover (talk) 19:43, 16 April 2020 (UTC)
 * , no, as far as I know, in Soviet Union people did not study this class of spaces. And the term "stereotype space" appeared in 90ies. But I don't understand this concern about the term. It is usual in mathematics that people suggest new terms. For example, the term quantum group appeared not long ago. I only heard it in 90ies. Outside of Russia these spaces were called "polar reflexive spaces". The book by Köthe was not translated into Russian, that is why it did not occur to anybody here to use this combination of words. And that is why it did not occur to me to mention this in the article. Eozhik (talk) 20:19, 16 April 2020 (UTC)
 * If you have offline 90's era Russian sources using the term, could you cite them for us and give short quotes? Epiphyllumlover (talk) 20:23, 16 April 2020 (UTC)
 * I have edited the format of Eozhik's post for making understandable the change of paragraphs. I hope to not having changed the meaning.
 * Please, do not discuss other's posts, discuss the content of the article. For being clear, my point is firstly that there are important results on duality of topological vectors published by Grothendieck, Bourbaki, and other members of Bourbaki group ("important" is not my own opinion, as these result are a part of the motivation of Grothendieck's Field medal). Secondly, these results are not cited in the articles. Thirdly nothing is said in the article for distinguishing Akbarov own results from those that must be credited to others (the fact that Akbarov papers have been accepted by editors means that some results are new, not that they are all new). Thus the Wikipedia article does not follows the Wikipedia policy of neutral point of view (see WP:NPOV). None of these points is addressed in Eozhik's answer. D.Lazard (talk) 20:43, 16 April 2020 (UTC)


 * , it would be good if you would not edit my text. It is not yours. There is no intersection between the results listed in the article and Bourbaki's texts. This happens in mathematics. Eozhik (talk) 21:02, 16 April 2020 (UTC)
 * Agreed that D.Lazard should not edit Eozhik's posts. I hope Eozhik will not be too distracted by this to answer my question about whether he has offline 90's era Russian sources using the term and if he could you cite them for us. To D.Lazard: If we do not delete the article, maybe it can be improved somewhere along the lines you suggest. I think there could be room for compromise.--Epiphyllumlover (talk) 21:22, 16 April 2020 (UTC)
 * , no, I don't know papers in Russian where this term is used (and which don't belong to our group). But you know, it seems to me you take what happens more serious than I do. This is not the end of the world. I just wanted to do what I can, and that is all. Eozhik (talk) 21:33, 16 April 2020 (UTC)
 * D.Lazard has a valid point that several of the results come from elsewhere, e.g. basically all of the Examples section. The claim that There is no intersection between the results listed in the article and Bourbaki's texts is dubious: Chapter IV of Bourbaki's Topological Vector Spaces has significant intersection, including several entire sections after section 3 which begins with: A locally convex space E is said to be reflexive if the canonical mapping cE from E into E" is a topological vector space isomorphism from E onto the strong dual of Eb~. Some of the example in this article are facts given in Bourbaki, e.g. Definition 4 - A locally convex Hausdorff and barrelled space in which every bounded subset is relatively compact is called a Montel space (i.e. X Montel if and only if X barrelled + Heine-Borel; for locally convex X), Proposition 9 - The strong dual of a Montel space is a Montel space. (i.e. X Montel if and only if X* Montel), or Corollary - The bidual of a locally convex metrizable space is a Frechet space. There's certainly unattributed overlap and dependence on earlier results. I don’t think that this isn a major concern in terms of the delete/keep discussion though, that’s moreso a cleanup point. — MarkH21talk 21:55, 16 April 2020 (UTC)
 * Dubious? In Bourbaki's book reflexive spaces are defined by tradition, i.e. as those for which the mapping $$E\to E$$ is an isomorphism, where $$E'$$ and $$E$$ are endowed with the strong topology (i.e. the topology of uniform convergence on bounded sets). And the results on duality are either about weak diality, or about strong duality. Not about the duality where the dual $$E'$$ and the bidual $$E''$$ spaces are endowed with the topology of uniform convergence on totally bounded sets. Which proposition in the article is contained in Bourbaki, ? Eozhik (talk) 22:41, 16 April 2020 (UTC)
 * The point was that some of the content, e.g. much of the "Examples" section, come directly from older sources like Bourbaki. Otherwise, you're claiming that it is entirely your original result that X is a Montel stereotype space if and only if X* is a Montel stereotype space, or that X is a Montel stereotype space if and only if X is a barrelled and Heine-Borel stereotype space. These examples are based on the works covered in Bourbaki. — MarkH21talk 08:01, 18 April 2020 (UTC)
 * For Montel spaces and their strong duals the topology of unform convergence on totally bounded sets coincides with the usual strong topology on X*, so this result becomes indeed trivial:"X is a Montel stereotype space if and only if X* is a Montel stereotype space" I gave it for the completeness of the picture. And this is just a definition of Montel spaces: "X is a Montel stereotype space if and only if X is a barrelled and Heine-Borel stereotype space" Maybe it should be omited. Each Montel space is stereotype, and this follows from its definition and from the fact that each quasicomplete and barreled space is stereotype. This statement belongs as far as I remember, to W.C.Waterhouse. I don't know, perhaps one should mention this in the article. Eozhik (talk) 08:42, 18 April 2020 (UTC)
 * Montel spaces are in addition reflexive in the usual sense. So the fact that they are stereotype follows from M.F.Smith's results. One can say that she is the author. I agree that this section could be filled with more references. Eozhik (talk) 08:57, 18 April 2020 (UTC)


 * Comment, as a lay person looking at the article it appears way too WP:TECHNICAL, belonging in a journal on mathematics, not an encyclopedia. Coolabahapple (talk) 03:05, 18 April 2020 (UTC)
 * , it is normal for articles on mathematics. Look at the articles in "Encyclopedia of Mathematics", they are all technical. Eozhik (talk) 03:47, 18 April 2020 (UTC)
 * In what people write here I see a reasonable reproach that this article reflects mostly the point of view of a group of specialists from one country, Russia. Formally all views must be represented, including other people's understanding of what these spaces must be called. To clear my conscience, and if no one objects, I will add the term "polar reflexive space" and a link to the Köthe book. Eozhik (talk) 03:56, 18 April 2020 (UTC)
 * I did this., if you are still seeking intersections with the results of Grothendieck, this is hopeless. There are no such intersections. Our general reproach to him is exactly that he did not pay attention to the results of M.F.Smith and others, and did not understand the importance of this class of spaces which simplifies everything. Eozhik (talk) 04:21, 18 April 2020 (UTC)
 * The Encyclopedia of Mathematics is a technical source, moreso than Wikipedia is supposed to be.I am not claiming that the results described in this article are due to Grothendieck, but just adding to 's point some of the content here is based on older works not referenced here (see the comments above about the "Examples" section). As mentioned before though, it's really a cleanup issue and not the deletion argument so we shouldn't focus on it. — MarkH21talk 08:05, 18 April 2020 (UTC)
 * That is why the author wrote a preamble in this article. This is the usual style for such cases, . Eozhik (talk) 05:58, 23 April 2020 (UTC)


 * Keep it! This article reveals so many ways to get around the difficulties of locally convex spaces! It is tremendously useful for anyone looking at the subject and wondering, "Is there a better way?" It garners interest in a subject that would otherwise be dead (topological vector space duality) by providing a fresh perspective. I never would have discovered it by looking at the journal articles. Isn't Wikipedia all about creating community around ideas? Wham Bam Rock II (talk) 07:30, 20 April 2020 (UTC) — Note: An editor has expressed a concern that Wham Bam Rock II (talk • contribs) has been canvassed to this discussion.
 * God sees everything, . Eozhik (talk) 06:40, 21 April 2020 (UTC)
 * , I think you should explain how you found out about this discussion because it's not good to look blankly at this picture. Even in absurdity, there must be a measure. Eozhik (talk) 06:40, 21 April 2020 (UTC)
 * How else? I came to the page to look up some properties of stereotype spaces and saw that the article was about to be deleted! Wham Bam Rock II (talk) 02:18, 22 April 2020 (UTC)
 * Look, if you want proof that I'm not canvassed, here's what turns up when I search "topological vector space" in my Math PDFs folder: TVS math folder.png Wham Bam Rock II (talk) 02:33, 22 April 2020 (UTC)
 * Also, feel free to check my talk page. You'll see I've been a user since 2010. Wham Bam Rock II (talk) 02:33, 22 April 2020 (UTC)


 * , thank you and excuse me for what you see here. The owners of this club forgot to put a sign on the entrance: "Anyone entering here must be ready to play a role in our absurdist theater!" Eozhik (talk) 03:15, 22 April 2020 (UTC)


 * Redirect to Topological vector space per WP:PRESERVE and WP:RCHEAP. I haven't seen enough content for a standalone article. buidhe 03:26, 22 April 2020 (UTC)
 * Redirect instead of delete is a good point. Reflexive space may be a better more specific target. — MarkH21talk 03:49, 22 April 2020 (UTC)
 * Redirect per above (I change my !vote). This applies to the 3 articles under discussion. D.Lazard (talk) 09:39, 22 April 2020 (UTC)
 * To which target? — MarkH21talk 13:46, 22 April 2020 (UTC)
 * I don't know. D.Lazard (talk) 15:11, 22 April 2020 (UTC)
 * If the outcome of the AfD is a redirect, then we can discuss specific targets, I suppose. (I myself prefer deletion so a discussion like that is moot.) —- Taku (talk) 00:06, 23 April 2020 (UTC)


 * Redirect, with a slight preference to Reflexive space as the target. I don't think the case has been made that we need an entire article on this topic, let alone three. XOR&#39;easter (talk) 01:15, 23 April 2020 (UTC)


 * , until recently, they were two: Stereotype space and Stereotype algebra. Now they are three because for some unknown reason singled out part of the material from the article Group algebra of a locally compact group (which was called "Group algebra" before these manipulations) and created a separate article for it: Stereotype group algebra. This is a subject of separate perplexity for me because, in particular, the text describing group algebras of finite groups is no more relevant to stereotype algebras than to other group algebras. Why it must be eliminated from the article "Group algebra of a locally compact group" is a puzzle, I wrote this on the talk page. If the question of redirection is discussed now (and if by "redirection" people mean moving the text to another article), then it will be logical to move Stereotype group algebra back to Group algebra of a locally compact group. The closest article for Stereotype space is I think Reflexive space, and for Stereotype algebra —Topological algebra. At the same time, what are called "targets" here are elaborated worse than the articles that are redirected to them, I think this problem should also be discussed somehow. Eozhik (talk) 05:19, 23 April 2020 (UTC)


 * I also wanted to ask people what is meant by monographs here? Eozhik (talk) 06:04, 23 April 2020 (UTC)
 * Redirect or delete. The article lists ~20 non-inline references, not a single one however seems to use the article name it their title. --Piotr Konieczny aka Prokonsul Piotrus&#124; reply here 07:18, 23 April 2020 (UTC)


 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.