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A generalization of $ F$-spaces and some topological characterizations of GCH


Author: Mary Anne Swardson
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
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0709575-0
Keywords: $ {F_\alpha }$-spaces, $ \alpha $-basically disconnected, $ \alpha $-pseudocompact, $ {2^\alpha } = {\alpha ^ + }$, $ {\chi_\alpha }$-remote point, $ \alpha $-open, $ \alpha $-closed, almost compact, weak Lindelöf number
Article copyright: © Copyright 1983 American Mathematical Society

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