Federer–Morse theorem

In mathematics, the Federer–Morse theorem, introduced by, states that if f is a surjective continuous map from a compact metric space X to a compact metric space Y, then there is a Borel subset Z of X such that f restricted to Z is a bijection from Z to Y. Moreover, the inverse of that restriction is a Borel section of f—it is a Borel isomorphism.