An Extension of Banach's Mapping Theorem

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Feb 1969Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 20, page 520 (issn: 0002-9939,

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Authors: Brualdi, R. A.;

doi: 10.2307/2035690 , 10.1090/s0002-9939-1969-0236029-9

An Extension of Banach's Mapping Theorem

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Abstract

The following mapping theorem of Banach [I] is well known. It is the basis of most proofs of the Schroder-Bernstein equivalence theorem. If X and Y are sets and f: X-* Y and g: Y-*X are injective mappings, then there exists partitions2 X=X1+X2 and Y= Yi+ Y2 such that f (Xj) = Yi and g(Y2) =X2. The conclusion of this theorem can be rephrased in the following way. Let AC XX Y be the relation between X and Y defined by

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combinatorics

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