Talk:Separation axioms

I have a request: the explanation of the different usages of the terms in the literature is useful, but we also need a standard usage guide for Wikipedia of those terms. I would suggest that we adopt the usage from the Topology glossary, make that the most prominent in this article, and then, in a separate section, explain how some people use the terms differently, and for what reasons.

Right now, as the article stands, I can not unambiguously use the term "regular topological space" in any Wikipedia article. AxelBoldt, Wednesday, April 3, 2002

The Topology Glossary deliberately doesn't define T₃ and T₄ because of this problem. I would prefer to use the stronger definitions for these, but I'm not sure what other people think. --Zundark, Thursday, April 4, 2002

Whatever terminology you think is the most standard, let's go with it. As long as we explain the other terminologies in this article, we should be fine. AxelBoldt

I'm pretty sure that what I've called the "modern convention"s in the article are the more standard today, as reflected in Axel's comment in the article's Glossary. So everything should be cool now. -- Toby Bartels (2002 April 24)

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Axel, I don't like having the word "space" in the entries to the table in the glossary, for two reasons:

1. It clutters the table.
2. I've noticed that even people that don't mind saying "Hausdorff space" or "Let X be Fréchet." still avoid saying "Fréchet space" (in this context), to avoid confusion with the other, more common meaning (which needs its own article ^_^).

If you think that it's unclear that the column labelled "Space" refers to the names given to spaces while the columns labelled "Axioms" refer to the names given to axioms, then I'd rather explain this with text before the table. — Toby Bartels, Wednesday, June 12, 2002

the reason I put in the "space" was because the table is so long that one usually doesn't see the table header, one only sees a row like T4, T4+T0, T4. And I see the crucial point of the article to be the distinction between T4, the axiom, and T4, the space. How about if we put "space" in only for those entries where "X, the space" is different from "X, the axiom"? But it's your baby, so do what you think is best. AxelBoldt, Wednesday, June 12, 2002

Although I appreciate the thought, the "your baby" sentiment doesn't seem very Wikiish, does it? In any case, I think that your idea is good, so I'll implement it. — Toby Bartels, Thursday, June 13, 2002

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If anybody is watching this article: I intend to do a major rewrite for purposes of clarity of exposition. This will banish all talk of historical and variant meanings of terminology, fixing a specific language for all time, except for warnings and a link at the beginning. This link will be to a new page, History of the separation axioms, that will explain how the axioms were originally numbered and how the terminology has changed. (I even hope to look at some primary sources to research this!) In contrast, this page, Separation axiom, will have no ambiguities, not even between "T_i axiom" and "T_i space", and will agree with both Topology Glossary and (hopefully) usage in the rest of Wikipedia. — Toby 17:35 Jul 23, 2002 (PDT)

OK, this is done. I still have to write History of the separation axioms, which will incorporate some material from the old page that didn't make it into the new page. (I also have that on my own machine, so it is not lost!) Note that the page has been renamed following naming conventions to a singular noun, but I'm not going to move this talk page, since it's largely irrelevant to the new version. — Toby 20:54 Aug 5, 2002 (PDT)