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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Products of weakly-$\aleph$-compact spaces

Author: Milton Ulmer
Journal: Trans. Amer. Math. Soc. 170 (1972), 279-284
MSC: Primary 54D20
MathSciNet review: 0375232
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Abstract: A space is said to be weakly- ${\aleph _1}$ -compact (or weakly-Lindelöf) provided each open cover admits a countable subfamily with dense union. We show this property in a product space is determined by finite subproducts, and by assuming that ${2^{{\aleph _0}}} = {2^{{\aleph _1}}}$ we show the property is not preserved by finite products. These results are generalized to higher cardinals and two research problems are stated.

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Keywords: Weakly-Lindel&#246;f, weakly-<!– MATH $\mathfrak {n}$ –> <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\mathfrak {n}$">-compact, product spaces, nonmeasurable cardinals, generalized continuum hypothesis, Lusin’s hypothesis
Article copyright: © Copyright 1972 American Mathematical Society