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
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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 ${2^\alpha } = {\alpha ^ + }$ .References
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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