Talk:Separation axiom

From Wikipedia, the free encyclopedia

Note that an older version of this page existed at Separation axioms, but the page was completely redesigned for the move. There is old talk at Talk:Separation axioms, but this is largely irrelevant to the new page, so I haven't moved it. -- Toby 20:56 Aug 5, 2002 (PDT)

---

I removed both of the alternative definitions (one put in by me, one put in by Axel) in order to keep the emphasis on the relationships to various forms of separation -- what it is that joins all of these together as separation axioms. These alternative characterisations (and many more) may still be found on the axioms' individual pages. (I made it more clear before the definitions that this is so.) -- Toby Bartels 13:13 21 May 2003 (UTC)

---

I removed the word "continuous" from "separated by a function" in the section giving the definitions, since that word is not used in the introductory section on separation, nor in the phrase as defined on Separated sets. I'm not absolutely opposed to adding the word "continuous" throughout, although I would argue that it's unnecessary in a topological context (especially since, if you remove continuity from the definition given on Separated sets, the notion becomes trivial). -- Toby Bartels 23:45, 2005 Jan 31 (UTC)

---

Fully normal does not imply regular. On the other hand, for a Hausdorff space, full normality and paracompactness are equivalent. Manta 21:51, 19 December 2006 (UTC)

Do you know of a specific counterexample (a space that's fully normal but not regular)? But to be honest, I doesn't strike me as at all likely that full normality should imply regularity, and since I appear to be the one that originally put that word in, I think that I'd better remove it. Still, if there is a specific counterexample that inspired you to make this comment, it would be nice if you mentioned it here.

And while I'm giving you advice: as long as you're sure of your facts (well, subject to NPOV and verifiability), then you should be bold and edit the page yourself! ^_^

—Toby Bartels 19:12, 9 May 2007 (UTC)

Ha!, I see that you gave an example on Talk:Paracompact space: Sierpinski space. So I am quite satisfied; you are entirely correct! —Toby Bartels 19:23, 9 May 2007 (UTC)

[edit] T_1/2 spaces?

I have a book "Topological Methods in Chemistry" by Merrifield and Simmons that discusses T_1/2 spaces. By their definition, a space is a T_1/2-space if each point of the space is either open or closed or both. This notion was used for a discussion of finite topologies. It is claimed that T_1/2 spaces are truly intermediate between T₀ and T₁ spaces in the sense that all T₁ spaces are T_1/2 and all T_1/2 spaces are T₀ and there exist weaker topologies that do that satisfy the stronger. However this separation axiom is not reflected in this article. Jason Quinn 00:30, 2 June 2007 (UTC)

Then please, be bold and put it in! Cite Merrifeld and Simmons as your reference in the Sources section. If you don't know how it fits in to the diagram or the discussion on T₀ vs non-T₀, then just place it in the section on Other separation axioms. This article should be comprehensive, so the more the merrier! --Toby Bartels 22:33, 14 June 2007 (UTC)