Gerlits, J.; Hajnal, András; Szentmiklóssy, Zoltán On the cardinality of certain Hausdorff spaces. (English) Zbl 0766.54002 Discrete Math. 108, No. 1-3, 31-35 (1992). Summary: We prove (in ZFC) the following theorem. Assume \(\kappa\) is an infinite cardinal, \(X\) is a Hausdorff space such that every subspace \(Y\) of \(X\) is the union of \(\kappa\) compact subsets of \(Y\). Then \(X\) has cardinality at most \(\kappa\). Cited in 1 ReviewCited in 2 Documents MSC: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.) Keywords:ZFC; cardinality PDFBibTeX XMLCite \textit{J. Gerlits} et al., Discrete Math. 108, No. 1--3, 31--35 (1992; Zbl 0766.54002) Full Text: DOI References: [1] Arhangelskii, A., Constructions and classifications of topological spaces, Uspekhi Mat. Nauk, 35, 29-84 (1978), (in Russian) [2] Baumgartner, J., A new class of order types, Ann. Math. Logic, 9, 187-222 (1976) · Zbl 0339.04002 [3] Bregman, Iu.; Šhostak, A.; Šhapirovskii, B., A theorem on decomposition, Tartu Riikl. Ul Toimetised, 836, 79-90 (1989) [4] Gerlits, J.; Juhász, I., On left-separated compact spaces, Comm. Math. Univ. Carolinae, 19, 1, 53-62 (1978) · Zbl 0393.54016 [5] Hajnal, A., Proof of a conjecture of S. Ruziewicz, Fund. Math., 50, 123-128 (1961) · Zbl 0100.28003 [6] S. Shelah, Proper Forcing, Lecture Notes in Math. Vol. 940 (Springer, Berlin).; S. Shelah, Proper Forcing, Lecture Notes in Math. Vol. 940 (Springer, Berlin). · Zbl 0495.03035 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.