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- W2032906403 abstract "Recently I proved the following theorem: To every positive integer m there exists a positive integer h such that the following holds: If S is a set of h elements and f a mapping of the power set B of S into B such that f(T)⊆T for all TϵB, then there exists a strictly increasing sequence T1⊂…⊂Tm of subsets of S such that one of the following three possibilities holds: (a) All sets f(Ti), i=1,…,m, are equal. (b) For all i=1,…,m we have f(Ti)=Ti (c) Ti=f(Ti+1) for all i=1,…,m−1. The proof given in [2] was non-constructive. In this paper now we give a constructive proof. By the way, this also yields a solution of a problem of Rado [3, p. 106]." @default.
- W2032906403 created "2016-06-24" @default.
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- W2032906403 date "1983-01-01" @default.
- W2032906403 modified "2023-09-28" @default.
- W2032906403 title "A constructive proof for a theorem on contractive mappings in power sets" @default.
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- W2032906403 doi "https://doi.org/10.1016/0012-365x(83)90178-4" @default.
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