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A refinement of Cantor's theorem


Author: G. Kirmayer
Journal: Proc. Amer. Math. Soc. 83 (1981), 774
MSC: Primary 04A99
DOI: https://doi.org/10.1090/S0002-9939-1981-0630053-5
MathSciNet review: 630053
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Abstract: It is shown that there is no surjection from the one-element subsets of a set containing an infinite co-infinite set to the infinite co-infinite subsets of that set. It is also shown that there is no surjection from the one-element subsets of an infinite set to the infinite subsets of that set. The proof can be formalized in a subtheory of both Zermelo Set Theory and New Foundations (and thus makes no use of the Axiom of Choice).


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DOI: https://doi.org/10.1090/S0002-9939-1981-0630053-5
Article copyright: © Copyright 1981 American Mathematical Society

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