Federer–Morse theorem: Difference between revisions
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==References== |
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*{{Citation | last1=Federer | first1=Herbert | last2=Morse | first2=A. P. | title=Some properties of measurable functions | doi=10.1090/S0002-9904-1943-07896-2 | id={{MR|0007916}} | year=1943 | journal=[[Bulletin of the American Mathematical Society]] | issn=0002-9904 | volume=49 | pages=270–277}} |
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[[Category:Topology]] |
[[Category:Topology]] |
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Revision as of 18:34, 20 February 2012
In mathematics, the Federer–Morse theorem states that if f is a 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 f(X).
References
- 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, MR0007916