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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Products of weakly-$\aleph$-compact spaces
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by Milton Ulmer PDF
Trans. Amer. Math. Soc. 170 (1972), 279-284 Request permission

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
  • © Copyright 1972 American Mathematical Society
  • 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