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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
DOI: https://doi.org/10.1090/S0002-9947-1972-0375232-9
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0375232-9
Keywords: Weakly-Lindelöf, weakly- $ \mathfrak{n}$-compact, product spaces, nonmeasurable cardinals, generalized continuum hypothesis, Lusin's hypothesis
Article copyright: © Copyright 1972 American Mathematical Society