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

Products of $ \mathfrak{m}$-compact spaces


Authors: Victor Saks and R. M. Stephenson
Journal: Proc. Amer. Math. Soc. 28 (1971), 279-288
MSC: Primary 54.52
MathSciNet review: 0273570
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0273570-6
PII: S 0002-9939(1971)0273570-6
Keywords: Product spaces, countably compact spaces, $ \mathfrak{M}$-compact spaces, products of $ \mathfrak{M}$-compact spaces
Article copyright: © Copyright 1971 American Mathematical Society