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

References

  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

  • 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

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