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
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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
- W. W. Comfort and S. Negrepontis, Some topological properties associated with measurable cardinals, Fund. Math. 69 (1970), 191–205. MR 276103, DOI 10.4064/fm-69-3-191-205
- W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Die Grundlehren der mathematischen Wissenschaften, Band 211, Springer-Verlag, New York-Heidelberg, 1974. MR 0396267
- W. W. Comfort and S. Negrepontis, Continuous pseudometrics, Lecture Notes in Pure and Applied Mathematics, Vol. 14, Marcel Dekker, Inc., New York, 1975. MR 0410618
- H. H. Corson, The determination of paracompactness by uniformities, Amer. J. Math. 80 (1958), 185–190. MR 94780, DOI 10.2307/2372828
- Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
- H. J. Keisler and A. Tarski, From accessible to inaccessible cardinals. Results holding for all accessible cardinal numbers and the problem of their extension to inaccessible ones, Fund. Math. 53 (1963/64), 225–308. MR 166107, DOI 10.4064/fm-53-3-225-308
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