Given two sets X, Y and P ⊆ X × Y, a uniformization of P is a subset P* ⊆ P such that for all x ∈ X, 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 x ∈ A. Such an f is called a uniformizing function for P.
KeywordsPolish Space Borel Function Winning Strategy Uniformizing Function Uniformization Theorem
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