Federer–Morse theorem

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In mathematics, the Federer–Morse theorem, introduced by Federer and Morse (1943), 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.[1]

See also[edit]


  1. ^ Raymond C. Fabec (28 June 2000). Fundamentals of Infinite Dimensional Representation Theory. CRC Press. p. 12. ISBN 978-1-58488-212-1. 

Further reading[edit]

  • Cn. J. Math., Vol. XXXII No 2, 1980, pp441-448 A Functional Analytic Proof of a Selection Lemma. L. W. Baggett and Arlan Ramsay