×

Cardinalities of ccc-spaces with regular \(G_{\delta}\)-diagonals. (English) Zbl 1094.54001

Summary: We show that the cardinality of a ccc-space with a regular \(G_{\delta}\)-diagonal is at most \(2^{\omega}\).

MSC:

54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Arhangelskii, A. V., The structure and classification of topological spaces and cardinal invariants, Uspekhi Mat. Nauk, 33, 6 (204), 29-84 (1978), 272 (in Russian) · Zbl 0414.54002
[2] Engelking, R., General Topology, Sigma Ser. Pure Math., vol. 6 (1989), Heldermann: Heldermann Berlin · Zbl 0684.54001
[3] Ginsburg, J.; Woods, R. G., A cardinal inequality for topological spaces involving closed discrete sets, Proc. Amer. Math. Soc., 64, 2, 357-360 (1977) · Zbl 0398.54002
[4] Hajnal, A.; Juhász, I., Discrete subspaces of topological spaces, Indag. Math., 29, 343-356 (1967) · Zbl 0163.17204
[5] Kurepa, D., The Cartesian multiplication and the cellularity number, Publ. Inst. Math. Beograd, 2, 121-139 (1962) · Zbl 0127.25003
[6] Shakhmatov, D. B., No upper bound for cardinalities of Tychonoff c.c.c. spaces with a \(G_\delta \)-diagonal exists. An answer to J. Ginsburg and R.G. Woods’ question, Comment. Math. Univ. Carolin., 25, 4, 731-746 (1984) · Zbl 0572.54003
[7] Uspenskii, V. V., A large \(F_\sigma \)-discrete Fréchet space having the Souslin property, Comment. Math. Univ. Carolin., 25, 2, 257-260 (1984) · Zbl 0553.54001
[8] Zenor, Ph., On spaces with regular \(G_\delta \)-diagonals, Pacific J. Math., 40, 759-763 (1972) · Zbl 0213.49504
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.