Complete pairs of coanalytic sets
Volume 194 / 2007
Fundamenta Mathematicae 194 (2007), 267-281
MSC: Primary 54H05; Secondary 03E15, 28A05.
DOI: 10.4064/fm194-3-4
Abstract
Let $X$ be a Polish space, and let $C_0$ and $C_1$ be disjoint coanalytic subsets of $X$. The pair $(C_0, C_1)$ is said to be complete if for every pair $(D_0,D_1)$ of disjoint coanalytic subsets of $\omega^\omega$ there exists a continuous function $f:\omega^\omega \to X$ such that $f^{-1}( C_0) = D_0$ and $ f^{-1}( C_1) = D_1$. We give several explicit examples of complete pairs of coanalytic sets.
