Baire Category

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


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.


Topological Space Polish Space Winning Strategy Compact Hausdorff Space Countable Intersection 
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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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