Talk:Baire category theorem

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Mathematics rating:	Start Class	Mid Priority	Field: Foundations, logic, and set theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 02:08, 15 June 2007 (UTC)

Can someone reference the connection to the axiom of choice? Gady 21:58, 12 Nov 2004 (UTC)

[edit] Too technical!

This article needs a naive statement of the theorem too. It should be possible for someone to look at this article and get something out of it without having to reference the Baire Space article. Ewjw 17:44, 8 August 2006 (UTC)

Yes, IMHO the article is needlessly confusing for readers who are coming here just for the Baire Category Theorem for complete metric spaces (which are presumably most readers). I propose removing most of the references to Baire spaces and mentioning it as a generalization. Functor salad 18:40, 27 September 2007 (UTC)

[edit] Irrational numbers complete??

In Section "Statement of the theorem", is the example given in the last paragraph correct?

I think an explanation is hinted at in the first paragraph of the section The set of all irrationals in irrational number. It depends on the metric; the space of irrational numbers becomes complete if you use a nonstandard metric. I'm not sure of this though; hopefully somebody can confirm this. -- Jitse Niesen (talk) 04:08, 9 October 2006 (UTC)

[edit] axiom of choice

may i suggest that section undergo some expansion. although it's obvious that the axiom of countable choice is required in the usual proof of Baire category theorem, would be good to point that out. a few remarks about why Baire category theorem implies axiom of dependable choice, if doable, might be good also. Mct mht 08:09, 31 May 2007 (UTC)