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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A generalization of $F$-spaces and some topological characterizations of GCH
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by Mary Anne Swardson
Trans. Amer. Math. Soc. 279 (1983), 661-675
DOI: https://doi.org/10.1090/S0002-9947-1983-0709575-0

Abstract:

Several topological characterizations involving $F$-spaces of the continuum hypothesis are due to R. G Woods and E. K. van Douwen. We extend this work by defining a space $X$ to be an ${F_\alpha }$-space if the union of $< \alpha$ cozero-sets is ${C^{\ast }}$-embedded in $X$ and by giving, for every infinite cardinal $\alpha$, topological characterizations involving ${F_\alpha }$-spaces of the cardinal equality ${2^\alpha } = {\alpha ^ + }$ .
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Bibliographic Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 279 (1983), 661-675
  • MSC: Primary 54G05; Secondary 54A25, 54A35, 54C45
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0709575-0
  • MathSciNet review: 709575