Products of weakly-ℵ-compact spaces

Ulmer, Milton

doi:10.1090/S0002-9947-1972-0375232-9

Products of weakly-$\aleph$-compact spaces
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by Milton Ulmer

Trans. Amer. Math. Soc. 170 (1972), 279-284

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

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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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