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Proceedings of the American Mathematical Society

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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
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.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1980 American Mathematical Society

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