Uniformization Theorems

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


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.




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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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