User talk:Topology Expert/Archive 6

Leads
Hi Topo, It is not always necessary to write an informal definition of a concept prior to giving the formal definition. This is only useful if the informal definition is likely to be sufficiently clear and easy so that people who do not read the formal definition can get something out of it. For example, if in the informal definition you say that f is restricted to some $$L^p$$ space and in the formal definition you say that it restricted to $$L^\infty$$, then you might as well say $$L^\infty$$ to begin with. Oded (talk) 04:10, 11 July 2008 (UTC)

Unsourced statements
While editing the article on one-point compactification, I noticed that you had included the statement

"If the one-point compactification of X is homeomorphic to the one-point compactification of Y, then X is homeomorphic to Y."

There was no inline citation or explanation given, which makes verifiability difficult. It would have taken a long time to search through all three references you gave to find the proof. In fact, I hope (and expect) that none of those references have this statement at all, since it is not true. Consider for instance X = [0,1) and Y = [0,1) u (1,2].

It seems that this is not an isolated example: many of your articles contain unsourced statements that turn out to be incorrect. I think it is a good idea for everyone to write with the goal that every nontrivial assertion comes either with a clear citation, a brief, convincing mathematical explanation, or both. Can you please try to do this? Plclark (talk) 10:52, 11 July 2008 (UTC)Plclark


 * As per your request, I found some mistakes in your article sequentially compact space and am bringing them to your attention.

1) Your definitions of sequence and subsequence are not correct: a sequence is not the range of a function but the function itself.

2) You wrote "This follows from the fact that every compact space is sequentially compact" and did not give a reference. The article compact space has a counterexample.  Plclark (talk) 11:02, 13 July 2008 (UTC)Plclark


 * I responded to your response on my own talk page, but perhaps it should appear here as well:


 * As I said, the article compact space contains the example $$\{0,1\}^c$$ with the product topology as an example of a compact space which is not sequentially compact. Previously it was unsourced, but I added a citation to an article of Scarborough and Stone which gives this example (with proof). On p. 209 of Ryszard Engelking's General Topology, he gives the Stone-Cech compactification of the natural numbers as another

example, with proof.


 * Your response to this issue is a good example of what I am talking about. You have claimed that compact implies sequentially compact is "obvious", but you have given neither any argument for it nor any clear citation.  You also say "according to Munkres' every compact space is sequentially compact" but you don't say where in Munkres' book this appears.  Thus in order to do verify (or, much more likely in this case, verify that it is not the case) this assertion I would have to read Munkres' book from cover to cover.  Previously you had claimed that Munkres defined a nowhere dense set as one with empty interior: again this is almost certainly not the case, but it would be very time consuming for someone else to check this.


 * I have thus far assumed good faith in all my dealings with you. However, your repeated insistence that standard references say things that they do not say in order to defend yourself is beginning to make me question that assumption.


 * Finally, of course I will be grateful for any mistakes you may find in my edits.


 * Plclark (talk) 04:27, 14 July 2008 (UTC)Plclark

By c I meant "continuum". Recall that I had referred you to this counterexample earlier; the full statement appears, with reference, in the article on compact spaces.

Again, I assumed good faith on your part even though records show that others have had issues with this in the past. Equivocating to try to demonstrate that I made a mistake (which in any case was not on an article) is not helping: surely you are not suggesting that if I can also make mistakes (which, of course, I can) then that excuses you from writing articles which are verifiable and correct?

I will ask you to fix these mistakes on sequentially compact space and to specifically retract your claims that Munkres says that nowhere dense subsets are by definition those with empty interior and that all compact spaces are sequentially compact. Otherwise there is no point in further discussion. Plclark (talk) 11:25, 14 July 2008 (UTC)Plclark

G_delta
Quite right, a slip of the pen. Thanks for pointing this out. Richard Pinch (talk) 06:30, 20 July 2008 (UTC)

You wrote "However, I have doubt as to whether User: Richard Pinch has obtained his definition from a reliable source." on another user's talk page. I would have appreciated it if you had raised the question directly with me at the same time. I took the definition directly from Steen and Seebach page 162, the reference at G-delta set. Richard Pinch (talk) 20:03, 8 August 2008 (UTC)

I am holding in my hand "Counterexamples in Topology", second edition by Lynn Arthur Steen and J. Arthur Seebach Jr. It is a yellow paperback published by Springer in 1978 with ISBN numbers 0-387-90312-7 and 3-540-90312. This is the reference I added to Gδ set in this edit (and which JackSchmidt changed to the Dover reprint, which I have not seen). The book is open at page 162, on which I see "A space in which every closed set is Gδ (or equivalently, every open set is Fσ) will be called a Gδ-space; a normal space which is also a Gδ-space is called (by Čech [29]) perfectly normal." This sentence is located in Part III, "Metrization Theory", in the second headed section "Basic Definitions". The term Gδ-space is in the index (p. 239) with a misprint but referring to page 162.

Furthermore, the Dover edition which is now in the references to that article happens to be accessible via Google books here. You will see that the highlighted sentence, on page162, is the one I quote. The term Gδ-space is again in the index (p. 239) with the misprint correct.

I am unable to understand how you can have failed to find this. If the book you have consulted has no page 162, then you simply cannot be looking at the right book.

Richard Pinch (talk) 06:55, 10 August 2008 (UTC)

Massey product
Hi, Please comment on the changes there. Katzmik (talk) 12:37, 16 September 2008 (UTC)

Sure.

Topology Expert (talk) 12:39, 16 September 2008 (UTC)


 * Hi, I initiated a discussion of a couple of points at the talk page there. Katzmik (talk) 09:07, 28 October 2008 (UTC)

Indentation
To make it easier to follow conversations, if someone posts a comment starting with a *, add two stars (**) at the beginning of your comment. That will give this effect:


 * Comment
 * Response

which is easy to follow. Also, most people place their signature directly after the end of their post, rather than on a different line. &mdash; Carl (CBM • talk) 13:14, 16 September 2008 (UTC)

Thanks for the advice, I will follow it in future.

Topology Expert (talk) 13:24, 16 September 2008 (UTC)


 * You can also use a colon at the front of the line to indent: that's the usual policy on Wikipedia. Xantharius (talk) 01:37, 17 September 2008 (UTC)