Talk:Zero-dimensional space
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Untitled[edit]
Should it be mentioned that the Animorphs books mention "Z-Space" a lot? Maybe "Z-Space" should redirect here.
-dogman15 02:38, 14 November 2006 (UTC)
- I think not :-). Zero-dimensional spaces are pretty cool in their own way, but you don't fly spaceships through them. --Trovatore 02:57, 14 November 2006 (UTC)
Moving to zero-dimensional (topology)[edit]
I intend to move this article to zero-dimensional (topology). In fact, the "about" template is not a sufficient dab, as non trivial zero-dimensional objects exists in algebraic geometry and commutative algebra (the zero-dimensional commutative Noetherian rings are exactly the Artinian rings and the zero-dimensional reduced commutative rings are exactly the commutative von Neumann regular rings). After the moving, I'll create the pages zero-dimensional (algebraic geometry), zero-dimensional (commutative rings), (probably the same page through a redirect) and zero-dimensional (disambiguation). D.Lazard (talk) 16:24, 17 March 2012 (UTC)
- I'm opposed. First of all, per WP:NOUN, article titles should not be adjectives. That's why this is at zero-dimensional space, not just zero-dimensional. Now, once the word space is there, those other objects are pretty clearly not what's intended. --Trovatore (talk) 19:26, 17 March 2012 (UTC)
Perhaps your real concern is the fact that zero-dimensional is a redirect to this page? That's a separate issue. I have no problem with you creating a zero-dimensional commutative ring article (note that it should be a noun, so this is better than the title you proposed, which was an adjective), and turning zero-dimensional into a disambig page. --Trovatore (talk) 19:38, 17 March 2012 (UTC)
- OK. But, in any case, Zero dimensional space is misleading, as most readers would guess "zero dimensional vector space". Thus I suggest to move to zero-dimensional topological space. D.Lazard (talk) 20:44, 17 March 2012 (UTC)
- Hmm, ya think? I kind of doubt that. Vector spaces aren't usually just called spaces — most of the time, space means topology. Besides, the zero-dimensional vector space is not really an encyclopedic topic at all. --Trovatore (talk) 21:05, 17 March 2012 (UTC)
- First of all, topological spaces and the topological definition of dimensions are quite recent invention, about 100 years ago, but geometrical and algebraic spaces are known for centuries. By no means could space means topology "most of the time". Maybe surprisingly for Trovatore, but the common name of a Euclidean space is still Euclidean space, the common name of an affine space is affine space, and the common name of a vector space is vector space (or "linear space"), and these names of categories are sometimes omitted, such as in three-dimensional space. Search queries https://www.google.com/search?q=two+dimensional+space and https://www.google.com/search?q=three+dimensional+space give little results on topological dimensions, but many results on aforementioned geometrical and algebraic constructs. Next, I hope that any single user is not charged to discreet between "really encyclopedic topic" and "not really encyclopedic topic" in English Wikipedia. There are many publications about vector space categories Vectk, FinVectk and TVectk where such "not really encyclopedic space" as zero-dimensional vector space k0 is the zero object. A general nonsense, one could say? So, what about empty matrices which occur in numerous applications of the matrix calculus? What about zero kernels and cokernels? I know, some users are not learned to distinguish between "(mathematically) trivial" and "nothing to say about", it is a harmful error which has to be eradicated from Wikipedia. Incnis Mrsi (talk) 09:07, 18 March 2012 (UTC)
- Euclidean space has a topology, which is pretty essential to the notion of Euclidean space, so I'm not sure what you're talking about. Yes, vector space is the usual name, but vector space specifically, not just space. Three-dimensional space is almost never an abstract 3d vector space, but rather R^3, which certainly has a topology.
- I can't really follow the part starting with Next, I hope that any single user.... I am skeptical that there's enough to say about the zero-dimensional vector space to be worthy of an article, but even supposing that there is, I think it's clear that that one should be called zero-dimensional vector space, whereas zero-dimensional space unmodified is an appropriate name for the topological notion. --Trovatore (talk) 12:52, 18 March 2012 (UTC)
- The problem is not that the usual spaces are or not topological spaces: every space has a topology, at least the discrete one. The problem is that the article is about the topological dimension zero and the title does not warn the reader that this is not the dimension that he/she has heard of before. I know that, in most usual cases, the topological dimension equals the usual dimension, but this equality is not evident from the definitions and not even made explicit in the article. Myself for example, although I did know the existence of topological dimensions, I was very surprised when I have read this article that it was very different from what was suggested by the title. Note also that, in the article, this is not its title which appears in boldfaace, but zero-dimensional topological space. D.Lazard (talk) 13:43, 18 March 2012 (UTC)
- First of all, topological spaces and the topological definition of dimensions are quite recent invention, about 100 years ago, but geometrical and algebraic spaces are known for centuries. By no means could space means topology "most of the time". Maybe surprisingly for Trovatore, but the common name of a Euclidean space is still Euclidean space, the common name of an affine space is affine space, and the common name of a vector space is vector space (or "linear space"), and these names of categories are sometimes omitted, such as in three-dimensional space. Search queries https://www.google.com/search?q=two+dimensional+space and https://www.google.com/search?q=three+dimensional+space give little results on topological dimensions, but many results on aforementioned geometrical and algebraic constructs. Next, I hope that any single user is not charged to discreet between "really encyclopedic topic" and "not really encyclopedic topic" in English Wikipedia. There are many publications about vector space categories Vectk, FinVectk and TVectk where such "not really encyclopedic space" as zero-dimensional vector space k0 is the zero object. A general nonsense, one could say? So, what about empty matrices which occur in numerous applications of the matrix calculus? What about zero kernels and cokernels? I know, some users are not learned to distinguish between "(mathematically) trivial" and "nothing to say about", it is a harmful error which has to be eradicated from Wikipedia. Incnis Mrsi (talk) 09:07, 18 March 2012 (UTC)
- Hmm, ya think? I kind of doubt that. Vector spaces aren't usually just called spaces — most of the time, space means topology. Besides, the zero-dimensional vector space is not really an encyclopedic topic at all. --Trovatore (talk) 21:05, 17 March 2012 (UTC)
In general, I believe that article titles are not supposed to be adjectives, according to the MOS. — Carl (CBM · talk) 23:26, 17 March 2012 (UTC)
- So what? Nouns or adjectives, but the problem requires a solution. Incnis Mrsi (talk) 09:07, 18 March 2012 (UTC)
Which converse?[edit]
The section Properties of spaces with small inductive dimension zero begins with this paragraph:
"A zero-dimensional Hausdorff space is necessarily totally disconnected, but the converse fails. However, a locally compact Hausdorff space is zero-dimensional if and only if it is totally disconnected."
It is not clear what the word "converse" refers to in the first sentence.
Is the (not necessarily true) converse this statement: "A totally disconnected Hausdorff space is zero-dimensional" ?
If so, this is not at all clear from the current phrasing. The phrase could mean the converse is "A totally disconnected set is zero-dimensional and Hausdorff".)
I hope that someone knowledgeable about this subject will clarify this issue. — Preceding unsigned comment added by 2601:200:c082:2ea0:6115:5f27:a5ac:8057 (talk) 06:44, 9 April 2024 (UTC)