Representing spaces as images of zero-dimensional spaces

Abstract

The following result is obtained, and is then applied to give a new proof of a set-valued selection theorem: For every nonempty Tychonoff space Y there exists a Tychonoff space X with dim X = 0, a perfect map f : X → Y, and a paracompact S ⊂ X with dim S = 0, such that f(S) = Y and f ∣ S is open.