Baire Category

Abstract

Let X be a topological space. A set A ⊆ X is called nowhere dense if its closure Ā has empty interior, i.e., Int(Ā) = Ø. (This means equivalently that X\Ā is dense.) So A is nowhere dense iff Ā is nowhere dense. A set A ⊆ X is meager (or of the first category) if A=⋃_n∈ℕ A _n , where each A _n is nowhere dense. A non-meager set is also called of the second category. The complement of a meager set is called comeager (or residual). So a set is comeager iff it contains the intersection of a countable family of dense open sets.