Classical Descriptive Set Theory pp 41-57 | Cite as

# Baire Category

Chapter

## 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.

### Keywords

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## Copyright information

© Springer-Verlag New York, Inc. 1995