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Baire Category

  • Alexander S. Kechris
Part of the Graduate Texts in Mathematics book series (GTM, volume 156)

Abstract

Let X be a topological space. A set AX 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

Authors and Affiliations

  • Alexander S. Kechris
    • 1
  1. 1.Alfred P. Sloan Laboratory of Mathematics and Physics Mathematics 253-37California Institute of TechnologyPasadenaUSA

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