# Talk:Baire space

From Encyclopedia of Mathematics

"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)

**How to Cite This Entry:**

Baire space.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Baire_space&oldid=27324