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An Elementary Proof of a Generalization of Banach’s Mapping Theorem

Ming-Chia Li
The American Mathematical Monthly
Vol. 121, No. 5 (May 2014), pp. 445-446
DOI: 10.4169/amer.math.monthly.121.05.445
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.05.445
Page Count: 2
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Abstract

Abstract We give an elementary proof of a generalization of Banach’s mapping theorem, which says that for any two mappings f : A → B and g : B → A, there exists a subset A0 of A such that g(B\f(A0)) = A\A0.

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