Swardson, Mary Anne A generalization of F-spaces and some topological characterizations of GCH. (English) Zbl 0535.54023 Trans. Am. Math. Soc. 279, 661-675 (1983). E. van Douwen, using earlier results of the reviewer, established several topological characterizations of the continuum hypothesis involving topological properties of F-spaces X for which \(| C^*(X)| =c\). Let \(\alpha\) be an infinite cardinal. The author defines an \(F_{\alpha}\)-space to be a Tychonoff space X in which the union of \(<\alpha\) cozero-sets of X is \(C^*\)-embedded in X (thus F-spaces are \(F_{\aleph_ 0}\)-spaces). She then characterizes the cardinal equality \(2^{\alpha}=\alpha^+\) by using topological properties of \(F_{\alpha}\)-spaces, thereby generalizing the work of the reviewer and van Douwen. Reviewer: R.G.Woods Cited in 1 ReviewCited in 2 Documents MSC: 54G05 Extremally disconnected spaces, \(F\)-spaces, etc. 54C45 \(C\)- and \(C^*\)-embedding 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) Keywords:weak Lindelöf number; F-spaces; \(F_{\alpha}\)-space; cozero-sets; cardinal equality PDFBibTeX XMLCite \textit{M. A. Swardson}, Trans. Am. Math. Soc. 279, 661--675 (1983; Zbl 0535.54023) Full Text: DOI