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.
