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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A topological characterization of a class of cardinals


Author: Rodolfo Talamo
Journal: Proc. Amer. Math. Soc. 80 (1980), 363-366
MSC: Primary 54A25; Secondary 03E55, 54D60
DOI: https://doi.org/10.1090/S0002-9939-1980-0577775-1
MathSciNet review: 577775
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Abstract: Let $ \mathfrak{m}$ be the first measurable cardinal. We say that a cardinal $ \alpha $ is Ulam-stable if, on the discrete space $ D(\alpha )$ of cardinal $ \alpha $, every filter with $ \mathfrak{m}$-intersection property can be extended to an ultrafilter with $ \mathfrak{m}$-intersection property. The main result we prove is the following: $ \alpha $ is Ulam-stable if and only if its Hewitt-Nachbin realcompletion $ \upsilon D(\alpha )$ is paracompact.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0577775-1
Article copyright: © Copyright 1980 American Mathematical Society