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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 equivalence of the singular cardinals hypothesis
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by M. Ismail and A. Szymanski
Proc. Amer. Math. Soc. 123 (1995), 971-973
DOI: https://doi.org/10.1090/S0002-9939-1995-1285997-0
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Abstract:

We show, in particular, that the Singular Cardinals Hypothesis is equivalent to the following statement: for each metric space X of cardinality greater than the continuum and of weigh of uncountable cofinality, the cardinality of X equals the weight of X.
References
  • Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
  • I. Juhász, Cardinal functions in topology, Mathematical Centre Tracts, No. 34, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg. MR 0340021
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Bibliographic Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 971-973
  • MSC: Primary 03E10; Secondary 03E65, 54A25
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1285997-0
  • MathSciNet review: 1285997