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

Topological Space Polish Space Winning Strategy Compact Hausdorff Space Countable Intersection
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag New York, Inc. 1995