Talk:Tychonoff's Theorem Without Choice

Recommend this is renamed to the site standard "Tychonoff's Theorem/Proof n" leaving this page name as a useful redirect. Then the Tychonoff's Theorem page can be enhanced so as to transclude the various proofs with or without AoC as appropriate. --prime mover (talk) 11:53, 2 January 2013 (UTC)

I guess? The three versions are not equivalent, so calling them three proofs of Tychonoff's theorem is a bit disingenuous. I would oppose transcluding the entire (rather long) proof of the ZF-only version, but if its statement could be brought down to a decent size that'd be fine. --Dfeuer (talk) 16:18, 2 January 2013 (UTC)

I'm also a huge fan of giving theorems the most descriptive names possible (while preserving common/traditional names), so calling the version for Hausdorff spaces "Tychonoff's Theorem/Proof 2" doesn't really sit well with me. Side note: I believe the version for Hausdorff spaces (using the ultrafilter lemma) was Tychonoff's original theorem, but the general version (using AoC) is the one most often cited as "Tychonoff's Theorem". The choice-free version must have come later and certainly is not of comparable historical significance. --Dfeuer (talk) 17:08, 2 January 2013 (UTC)

Yet another thing: there are a number of different proofs available, at least for the general case. Nets and Kelley's theorem can be used instead of filters and the ultrafilter lemma, and Kelley offers a proof I don't remember off the top of my head that does something else. There are probably plenty of others. It'd make more sense for those to get "proof 1", "proof 2", etc. --Dfeuer (talk) 19:41, 2 January 2013 (UTC)

Well you just do what you got to do, then. --prime mover (talk) 20:11, 2 January 2013 (UTC)

You could explain what it is you dislike about separate names for these theorems, suggest an alternative scheme that meets all needs, .....