An extension of Banach's mapping theorem, with applications to problems concerning common representatives
Published online by Cambridge University Press: 24 October 2008
Extract
In this paper, we give an extension (Theorem 1) of the following well-known result of Banach ((l)): If X, Y are sets and Θ: X → Y, ψ: Y → X are injective mappings, then there exist partitions X = X1 ∪ X2, Y = Y1 ∪ Y2 such that Θ(X1) = Y1 and ψ(Y2) = X2. Here, as is usual, we say that X = X1 ∪ X2 is a partition of the set X = X1 ∩ X2 = π. Our theorem is applied in sections 2 and 3 to problems concerned with the existence of common representatives for two families of sets.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 2 , April 1966 , pp. 187 - 192
- Copyright
- Copyright © Cambridge Philosophical Society 1966
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