Talk:Topology/Archive 1

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Archive This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

This is a question which pertains to the following as quoted from the article:

  • "The term topology is also used for a system of open sets used to define topological spaces, but this article will focus on the branch of mathematics".

Where can one find out about this definition which concerns "a system of open sets used to define topological spaces"? (Ericross)

In the topological space article. --Zundark 19:19 May 2, 2003 (UTC)

What's "equivariant jazz"? -- The Anome

I don't know, I took it out for now. --AxelBoldt

How do you define a limit of a sequence of points in a topological space? --Karl Palmen

A point x is a limit of a sequence (xn) if and only if the sequence is eventually in every neighbourhood of x. (That is, for every neighbourhood U of x, there are only finitely many n for which xn is not in U.) --Zundark, 2002 Jan 21

I've added several links to pages for terms that are referred to in the article and defined in the Topology Glossary. Many of these pages are nothing but redirects to that glossary, which people were told to be familiar with before reading past a certain point. I intend to write articles for most of these subjects that give more than just the definitions in the glossary but say something about what the concepts are good for and how they are used -- encylopedia stuff rather than dictionary stuff. In the meantime, they provide hotlinks to the glossary for anybody that thought that they were familiar with all of the terms but actually were not, which I think is useful. -- Toby Bartels

I wonder whether we should move all the material about "Topology - the structure" and the examples of topological spaces to topological space and reserve this article for the branch of mathematics? AxelBoldt, Thursday, June 6, 2002

I've often wondered the same thing, but haven't expressed it since I'm not up to doing the change myself yet. But I would approve. — Toby Bartels, Saturday, June 8, 2002

Topological space was probably the first page on Wikipedia that I created. I always thought that most of the content from Topology should be moved there, but I never got around to doing it. --Zundark, Sunday, June 9, 2002

Axel wondered what to do with the "useful theorems". I say, keep 'em here. I haven't looked at Topological_space yet, but what you have here now seems to belong here to me. — Toby Bartels, Tuesday, June 11, 2002


I just removed this:

Applications in science - The topology of the universe We do not yet know the global topology of the universe, and in fact may never be able to know what it is. However, some scientists, called cosmologists, are trying to measure cosmic topology using data from ground-based and space-based telescopes. Results from the MAP telescope may give an answer by 2002 or 2003. Or maybe not...

This doesn't fit in the topology article; I think it should probably go to manifold or pseudo-Riemannian manifold or differential geometry; this article is mainly about point-set topology which is unrelated. AxelBoldt 11:52 Aug 28, 2002 (PDT)

It's not that this article is unrelated, but that it's more general. It's not just the pseudo-Riemannian structure or even the differentiable structure that we don't know, but the topological structure itself is unknown. (Of course, this sense of "topology" is discussed at Topological space, not here.) I do agree that the paragraph doesn't belong in this article, but it would make a reasonable stub for an article Topology of the universe, which could even be listed here with a "See also". I think that I will make that stub now. — Toby 05:15 Sep 17, 2002 (UTC)

Does the term genus need to be used in the article someplace. A layman would say hole. A donut is genus one. A sphere is genus zero. Two16

I don't know that it needs to be here, but it should show up in algebraic topology and surface. -- Toby 05:41 Feb 9, 2003 (UTC)

I removed

and in fact the term "topologically equivalent" is mainly used when explaining topology to non-topologists.

on the grounds that I see analysts using this term (in a situation where you might have several types of equivalence running around, all called "«adverb» equivalent"). -- Toby 04:39 Mar 5, 2003 (UTC)

Yeah, and in hindsight it had a condescending air, too. Thanks. MightCould

True, but I didn't want to say that ^_^. But I forgot to mention that I like the elementary introduction -- that's the hardest part of writing this sort of article. -- Toby 10:19 Mar 8, 2003 (UTC)

I removed:

If you do, we have, for most fonts, the class {a,b,d,e,g,o,p,q} of letters with a hole, the class {c,f,h,k,l,m,n,r,s,t,u,v,w,x,y,z} of letters without a hole, and the class {i,j} of letters consisting of two pieces.

on the grounds that this heavily depends on assuming that the lines have non-zero width. I thought of just saying "for most fonts if you assume non-zero width" instead of just "for most fonts", but that could make the exercise seem a lot simpler than it really is.It's a much more involved problem to assume that their widths are zero, and that is when the font choice (especially serifs) comes into question. How can we rephrase this so as not to make the exercise seem too trivial? Do we need to give the answer at all? Or could there be a better exercise to use instead? -- Toby 17:34 Mar 19, 2003 (UTC)

"If you do" referred to "you consider the lines of each letter to have nonzero width", so it seems correct. Your second objection amounts to: "this is a rather simple problem, more complicated versions exist". I do not see why you delete this; you are welcome to discuss a more complicated version as well. - Patrick 17:55 Mar 19, 2003 (UTC)

Then I simply didn't understand the sentence; I thought it was if you do the problem. Let me try to come up with something clear, and you change it if it's bad. -- Toby 05:06 Mar 20, 2003 (UTC)

Okay, it is very clear now. - Patrick 09:50 Mar 20, 2003 (UTC)

Great! -- sorry that I took so long to get back to this. -- Toby 02:36 Apr 13, 2003 (UTC)

I think this page is long overdue some revision - too slanted towards algebraic topology, for one thing. Charles Matthews 16:27, 27 Apr 2004 (UTC)

Recent edit saying letter 'g' has two holes - I must be missing something (or a font...). Charles Matthews 10:31, 23 May 2004 (UTC)

You are thinking of a g like this: g\,. But serif fonts (like Times New Roman) typically have a g like this: \mathrm{g}\,. --Zundark 13:03, 23 May 2004 (UTC)

Well, that should perhaps be made clear; we can't rely on people reading the page in any given font. Charles Matthews 13:07, 23 May 2004 (UTC)

I would prefer to get rid of the whole paragraph. I don't see how it's helpful, and differences in fonts make it potentially confusing. --Zundark 13:20, 23 May 2004 (UTC)
An image of the alphabet in an applicable font could be added, or another set of examples can be presented.--Patrick 22:34, 23 May 2004 (UTC