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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
DOI: https://doi.org/10.1090/S0002-9939-1971-0273570-6
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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Keywords: Product spaces, countably compact spaces, <!– MATH $\mathfrak {M}$ –> <IMG WIDTH="27" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\mathfrak {M}$">-compact spaces, products of <!– MATH $\mathfrak {M}$ –> <IMG WIDTH="27" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$\mathfrak {M}$">-compact spaces
Article copyright: © Copyright 1971 American Mathematical Society