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Complete pairs of coanalytic sets

Jean Saint Raymond — 2007

Fundamenta Mathematicae

Let X be a Polish space, and let C₀ and C₁ be disjoint coanalytic subsets of X. The pair (C₀,C₁) is said to be complete if for every pair (D₀,D₁) of disjoint coanalytic subsets of ω ω there exists a continuous function f : ω ω X such that f - 1 ( C ) = D and f - 1 ( C ) = D . We give several explicit examples of complete pairs of coanalytic sets.

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