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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A topological characterization of a class of cardinals
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by Rodolfo Talamo
Proc. Amer. Math. Soc. 80 (1980), 363-366
DOI: https://doi.org/10.1090/S0002-9939-1980-0577775-1

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
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Bibliographic Information
  • © Copyright 1980 American Mathematical Society
  • 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