Definition talk:Tychonoff Separation Axioms

If these are actually Axioms, we should put them in the Axioms namespace. --Cynic (talk) 20:44, 10 January 2009 (UTC)
 * They're not. It's just what they're called, sort of like Europe is called a continent.  They are called the Separation Axioms because they are usually assumed in the statement of a proof about a space of a certain sort, but they aren't axioms in the sense that a=b implies b=a is an axiom. Zelmerszoetrop 06:59, 11 January 2009 (UTC)

Sorry to split hairs, but "a=b implies b=a" is only an axiom if you start with the numbers as a set of objects with a given set of properties. If you take as your axioms the Peano Postulates, for example, then "a=b implies b=a" can then be demonstrated. --Matt Westwood 10:22, 11 January 2009 (UTC)

That's beside the point, you knew what he meant. --Cynic (talk) 17:42, 11 January 2009 (UTC)

Turns out that putting a LaTeX formula in a heading doesn't work in a contents page. Shame, but there you go ... so I adjusted the heading names. --Matt Westwood 22:17, 23 February 2009 (UTC)

Is the last line of the definition correct? I would expect it to say "normal" there. --Matt Westwood 22:27, 23 February 2009 (UTC)

Sure, a mistake, I was just copying from above... Headings are ok like this, it is better to have a readable table of contents.--Cañizo 00:20, 24 February 2009 (UTC)

Further notes ... I've googled and can't find reference to this set of axioms being named for Kolmogorov. T0 appears to be, but collectively they seem to be named for Tychonoff (or Tikhonov, spelling varies), and even that's not universal. Should this page be renamed just "Separation Axioms"? --Matt Westwood 06:41, 24 February 2009 (UTC)

I agree, just leaved the title because it was already there. I'll do it.--Cañizo 19:00, 24 February 2009 (UTC)

Yep, just wanted confirmation, I know little about this area of maths beyond the basics of Hausdorff spaces. --Matt Westwood 20:37, 24 February 2009 (UTC)