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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
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.


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

  • [1] W. W. Comfort and S. Negrepontis, Some topological properties associated with measurable cardinals, Fund. Math. 69 (1970), 191-205. MR 0276103 (43:1851)
  • [2] -, The theory of ultrafilters, Springer-Verlag, New York, 1974. MR 0396267 (53:135)
  • [3] -, Continuous pseudometrics, Dekker, New York, 1975. MR 0410618 (53:14366)
  • [4] H. H. Corson, The determination of paracompactness by uniformities, Amer. J. Math. 80 (1958), 185-190. MR 0094780 (20:1292)
  • [5] L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
  • [6] H. J. Keisler and A. Tarsky, From accessible to inaccessible cardinals. Results holding for all accessible cardinal numbers and the problem of their extension to inaccessible ones, Fund. Math. 53 (1964), 225-308. MR 0166107 (29:3385)

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

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