Federer–Morse theorem

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

• Uniformization
• Hahn–Banach theorem

References

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

• 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

Further reading

• Cn. J. Math., vol. XXXII, no 2, 1980, pp. 441–448, A Functional Analytic Proof of a Selection Lemma. L. W. Baggett and Arlan Ramsay