Talk:Baire space

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"Any space in which the Baire category theorem on complete metric spaces is valid" — I am afraid, this may be puzzling: does it mean that "Baire" = "complete metric", or not? I see in a book (Kechris) such definition: a topological space in which the intersection of countably many dense open sets is dense. And then a proposition: an open subset of a Baire space is a Baire space. And then "The Baire Category Theorem: Every completely metrizable space is Baire. Every locally compact Hausdorff space is Baire." --Boris Tsirelson 16:22, 1 August 2012 (CEST)

In fact that was literally the old entry: I only changed the second portion because at a first glance the other made sense to me. But you are right and I've just changed it. As for the Baire category theorem I think most authors understand the bit on metric spaces: I anyway added the one on locally compact Hausdorff spaces for completeness. I will now add it to the other entry as well.Camillo 17:25, 1 August 2012 (CEST)
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