Talk:Tychonoff's theorem

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Where is it written never to use \empty?? Maybe this is true for HTML, where the empty set symbol doesn't fit well within a line of inline type. But, why should it not be used in math/tex mode when on a separate line?? The only possible reason I can think is because some might not render it, but this seems unlikely, if it renders tex, it should render \empty. And \empty is listed on the tex mark-up page. {} is good for inline, but silly for general policy, it's nonstandard to say the least. Revolver 20:29, 8 Jul 2004 (UTC)

I agree. Dyspropsia was the one who made this change, citing "Wikipedia conventions." I realise some browsers don't support the character, which discourages using it in text, but the software should (although it may not be) be smart enough to send these browsers inline images instead. In display-mode math it should always be used, although I've seen the alternate notation in some texts. Derrick Coetzee 02:18, 9 Jul 2004 (UTC)

I like this article. I think it would be better of "(also not altogether unexpected, since AC itself is equivalent to asserting whether or not an infinite product is empty!)" were replaced with "(also not altogether unexpected, since AC itself is equivalent to asserting that infinite product is non-empty!)". But I've never edited anything on Wikipedia, so I'm suggesting this here instead of making the change myself. -David

I've added your change, but in the future, Wikipedia:Be bold - you can't hurt anything. Thanks for your contribution. Deco 17:30, 27 January 2006 (UTC)

The article says that Tychonoff's theorem is complex - what does that mean? (Certainly it is always difficult to rigorously use the axiom of choice. But is this theorem harder than other applications?) I do not think that it is necessary for Tychonoff to be complex - if the properties of ultrafilters (sorry, "maximal sets with the finite intersection property") used are established in advance then a proof of Tychnoff can be very simple. But I am not a topologist - I know very little. What do other editors think of the proof? 128.135.100.27 03:44, 11 February 2006 (UTC)

Well, complexity is subjective. Perhaps it would be more accurate to say that "Known proofs of Tychonoff's theorem from first principles of topology are complex", but even then you might not think it's really all that complex. Maybe this statement should just be removed. Deco 04:49, 11 February 2006 (UTC)

It might be good to add the fairly simple proof using ultrafilters. I might add it. I think the statement that the Tychonoff theorem should be removed, since it's fairly simple to state and simple to prove (although the proof relies on a lot of more basic results). 67.71.22.78 03:46, 16 October 2006 (UTC) Jordan