# Baire spaces

## Idea

A Baire space is a topological space that satisfies the conclusion of the Baire category theorem?.

It should not be confused with the space of irrational numbers (sometimes called ‘Baire space’ and coincidentally an example of a Baire space in our sense) or a Baire set? (a subset somewhat analogous to a measurable set but defined by a topological property).

## Definition

A Baire space is a topological space such that the intersection of any countable family of dense open subspaces is also dense.

## Examples

Revised on June 30, 2011 01:23:37 by Toby Bartels (76.85.192.183)