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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.
- .Federer, Herbert; Morse, A. P. (1943), "Some properties of measurable functions", Bulletin of the American Mathematical Society, 49: 270–277, doi:10.1090/S0002-9904-1943-07896-2, ISSN 0002-9904, MR 0007916
- Baggett, Lawrence W. (1990), "A Functional Analytical Proof of a Borel Selection Theorem", Journal of Functional Analysis, 94: 437–450
- Cn. J. Math., Vol. XXXII No 2, 1980, pp441-448 A Functional Analytic Proof of a Selection Lemma. L. W. Baggett and Arlan Ramsay