Baire space
In mathematics, a topological space formula_1 is said to be a Baire space, if for any given countable collection formula_2 of closed sets with empty interior in formula_1, their union formula_4 also has empty interior in formula_1. Equivalently, a locally convex space which is not meagre in itself is called a Baire space. According to Baire category theorem, compact Hausdorff spaces and complete metric spaces are examples of a Baire space. Bourbaki coined the term "Baire space".