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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A topological equivalence of the singular cardinals hypothesis

Authors: M. Ismail and A. Szymanski
Journal: Proc. Amer. Math. Soc. 123 (1995), 971-973
MSC: Primary 03E10; Secondary 03E65, 54A25
MathSciNet review: 1285997
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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 [Enhancements On Off] (What's this?)

  • [Je] Thomas Jech, Set theory, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Pure and Applied Mathematics. MR 506523 (80a:03062)
  • [Ju] I. Juhász, Cardinal functions in topology, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg; Mathematical Centre Tracts, No. 34. MR 0340021 (49 #4778)

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Additional Information

PII: S 0002-9939(1995)1285997-0
Keywords: SCH, weight, tightness
Article copyright: © Copyright 1995 American Mathematical Society