A topological equivalence of the singular cardinals hypothesis

Ismail, M.; Szymanski, A.

doi:10.1090/S0002-9939-1995-1285997-0

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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

A topological equivalence of the singular cardinals hypothesis
HTML articles powered by AMS MathViewer

by M. Ismail and A. Szymanski PDF

Proc. Amer. Math. Soc. 123 (1995), 971-973 Request permission

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