Talk:General topology

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 Field: Topology
This article has comments.


I think set-theoretic topology deserves its own page. It is really distinct from general topology, in that it focuses on the results about topological spaces depending on set theoretic issues, whereas general topology seems to me to imply general topological concepts used everywhere (including set-theoretic, algebraic, differential topology, etc.) Revolver 11:50, 17 May 2005 (UTC)

In the beginning of the article it is stated that general topology is the same as point-set topology. But it is wrong because there is also pointless topology which also pertains to general topology. —Preceding unsigned comment added by Porton (talkcontribs) 18:16, 4 September 2007 (UTC)

This article is wrong. It says that General Topology is study of topological spaces, but General Topology also studies uniform spaces and proximity spaces. —Preceding unsigned comment added by Porton (talkcontribs) 16:03, 23 September 2007 (UTC)

Both which you mention are topological spaces. General topology is the study of topological spaces (a rather broad definition) and more specifically, the study of axioms that one can impose on them.--PST 10:21, 2 June 2009 (UTC)
Topological spaces is a term, not any space related to topology. A proximity space is not a topological space. (However it induces a topological space.) So the article is indeed wrong. VictorPorton (talk) 13:23, 25 May 2011 (UTC)
Also linear topological spaces, metric spaces, Banach and Hilbert spaces, Euclidean and non-Euclidean spaces, projective spaces etc., all are topological spaces; should they all be investigated by general topology? Boris Tsirelson (talk) 07:46, 25 July 2009 (UTC)

Rename to point set topology?[edit]

I find the title General topology confusing, as it gives the impression this could be a general page on topology which is really Topology. --Salix alba (talk) 07:47, 17 July 2006 (UTC)

  • I don't think so. First of all, this name is used commonly. And, secondly, whoever is interested in the topology article, rather than this one, can get there via the wikilink in the first sentence. --Kompik 15:38, 10 April 2007 (UTC)
General topology undermines numerous areas within mathematics: point-set topology, set-theoretic topology, continuum theory, topological dynamics, metrizability theory, topological algebra et cetera. --PST 08:53, 1 November 2009 (UTC)


Strangely enough, dimension is not mentioned; see Inductive dimension and Lebesgue covering dimension. Boris Tsirelson (talk) 07:38, 25 July 2009 (UTC)

Merge from point-set topology[edit]

I see that an ambitious editor has recently been writing a detailed article on point-set topology. At a glance, it looks like nice work (I haven't checked in any detail).

But I don't think that most workers make any serious distinction between point-set topology and general topology. I suppose general topology could also include pointfree topology, but that's a fairly minor sidelight IMHO.

So to recap, I think the new material is great, or at least is probably great (as I say, I haven't really checked), but I think it ought to be here, not there. I don't see any great value in having two articles on this topic. --Trovatore (talk) 02:58, 30 November 2013 (UTC)

Point-set topology was disambiguated because the term 'general topology' as used on Arxiv ( and other research math websites is much broader than just point-set topology. There are conferences with sessions dedicated to general topology, such as the Spring Topology and Dynamics Conference in Connecticut; topics this year included compactifications and continuum theory. I will follow the consensus.Brirush (talk) 03:07, 30 November 2013 (UTC)
Why are compactifications and continuum theory not part of point-set topology? --Trovatore (talk) 03:45, 30 November 2013 (UTC)
Touché. Anyway, I overreacted; I would be just fine merging the two, but it leaves a big disconnect between the research topics and the basic topics, and I had seen several people on this page argue they were different.Brirush (talk) 03:49, 30 November 2013 (UTC)
Oh, well, that's always a headache, I agree. But if they were split by level of difficulty, I'm not even sure which article should be more difficult. Is there a reason that gentop should be about research topics and PST about basic ones, or vice versa?
I don't have a good answer to the "level of difficulty" conundrum, but I doubt that it makes sense to split along those lines between these two titles. My current feeling, subject to being convinced otherwise, is that there should be a central article at one of the titles, and it should be mostly "basic", insofar as a subject that university math majors often first encounter in their third year can be "basic". Then articles about more specific topics can be linked to from that article, and they can be more advanced. --Trovatore (talk) 03:58, 30 November 2013 (UTC)
I think that that is very reasonable. You've given me some ideas. I can merge them if you like; I've written a mock-up on my user page: I've just added a 'research areas' sectiin under all the basics. I'm going to bed, but I'll merge them tomorrow unless you do it first or someone objects.Brirush (talk) 04:09, 30 November 2013 (UTC)
Looks beautiful, at a glance. I'll have to find some time and really read it. Thanks for your efforts! --Trovatore (talk) 20:14, 30 November 2013 (UTC)
Wow, the second paragraph is gorgeous. I think you've maybe come up with a solution for a longstanding issue in the lead of the compact space article; you might want to bring it up on that article's talk page (or perhaps I will). I'm not sure about the third (one-sentence) paragraph though — what does it mean? I'm tempted to say just leave it out. --Trovatore (talk) 21:38, 30 November 2013 (UTC)

Thank you; I really appreciate it. The third sentence was an afterthought,and it's getting the axe. Brirush (talk) 02:20, 1 December 2013 (UTC)

Summary of compactness[edit]

I know that we've had trouble summarizing the notion of compactness in an imprecise way on this site, but the summary given here is wrong. It says:

Compact sets are those that can be covered by finitely many sets of arbitrarily small size.

But, given ε>0, I can cover the open interval (0,1) with finitely many open intervals of length ε - yet (0,1) is certainly not a compact space.  J.Gowers  21:27, 4 June 2014 (UTC) — Preceding unsigned comment added by J.Gowers (talkcontribs)

Oh, right, that is kind of the natural reading, isn't it? I was thinking of it as a restatement of the every-open-cover-has-a-finite-subcover version, with the arbitrary open cover defining the "arbitrarily small size". But that's probably not intuitive to anyone not already used to that definition. Rats. I was so impressed when I first saw it. --Trovatore (talk) 21:33, 4 June 2014 (UTC)

Foundations of topology[edit]

I see such subsection (11.6), with only the link "Main article: Topology"; and I do not see anything like that in "Topology" article. What is meant by "Foundations of topology"? And more generally: separate foundations for each branch of mathematics? Or "federal" foundations of the whole mathematics? Boris Tsirelson (talk) 06:31, 6 February 2015 (UTC)

When I rewrote the article, I used online lists of topics related to general topology. I wasn't sure what "foundations of topology" was either. Feel free to omit it.Brirush (talk) 12:32, 6 February 2015 (UTC)
Well, if so, I just did. Whoever knows whats'it, feel free to insert it. Boris Tsirelson (talk) 15:28, 6 February 2015 (UTC)