Federer–Morse theorem

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Short description: On a property of surjective continuous maps between compact metric spaces


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.[1] Moreover, the inverse of that restriction is a Borel section of f—it is a Borel isomorphism.[2]

See also

References

  1. Section 4 of Parthasarathy (1967).
  2. Page 12 of Fabec (2000)

Further reading

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