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Uniformization Theorems

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

Abstract

Given two sets X, Y and PX × Y, a uniformization of P is a subset P* ⊆ P such that for all xX, Ǝ!yP(x,y) ⇔Ǝ!yP*(x,y) (where Ǝ! stands for “there exists unique”). In other words, P* is the graph of a function f with domain A = proj x (P) such that f(x) ∈ P x for every xA. Such an f is called a uniformizing function for P.

Keywords

Polish Space Borel Function Winning Strategy Uniformizing Function Uniformization Theorem 
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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