Federer–Morse theorem
From HandWiki
Revision as of 10:06, 9 May 2022 by imported>Rjetedi (change)
Short description: On a property of surjective continuous maps between compact metric spaces
 | This article provides insufficient context for those unfamiliar with the subject. (March 2017) (Learn how and when to remove this template message) |
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
- Baggett, Lawrence W. (1990), "A Functional Analytical Proof of a Borel Selection Theorem", Journal of Functional Analysis 94: 437–450
- Fabec, Raymond C. (2000). Fundamentals of Infinite Dimensional Representation Theory. CRC Press. ISBN 978-1-58488-212-1. https://archive.org/details/makingofearth00jone_0/page/12.
- 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
- Parthasarathy, K. R. (1967). Probability measures on metric spaces. Probability and Mathematical Statistics. New York-London: Academic Press, Inc..
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.
 |  |
