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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

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Products of $\mathfrak {m}$-compact spaces
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by Victor Saks and R. M. Stephenson PDF
Proc. Amer. Math. Soc. 28 (1971), 279-288 Request permission

Abstract:

Some results are given on the closure under suitably restricted products of a class of spaces similar to one considered by Z. Frolík and, more recently, by N. Noble. An answer is given to the following question of Gulden, Fleischman, and Weston: Does there exist $\mathfrak {M} > {\aleph _0}$ and an $\mathfrak {M}$-compact space $X$ such that some subset $A$ of $X$ of cardinality $\leqq \mathfrak {M}$ is contained in no compact subset of $X$? It is shown that for every $\mathfrak {M} \geqq {\aleph _0}$ there is a topological group which has this property.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 279-288
  • MSC: Primary 54.52
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0273570-6
  • MathSciNet review: 0273570