# Article

 Title: New properties of the concentric circle space and its applications to cardinal inequalities (English) Author: Sun, Shu-Hao Author: Choo, Koo-Guan Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 32 Issue: 2 Year: 1991 Pages: 395-403 . Category: math . Summary: It is well-known that the concentric circle space has no $G_\delta$-diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of $G_\delta$-diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities. (English) Keyword: concentric circle space Keyword: weak $G_\delta$-diagonal Keyword: point-separating $^\ast$-open cover Keyword: cardinal function MSC: 54A25 MSC: 54D20 MSC: 54G05 idZBL: Zbl 0772.54004 idMR: MR1137802 . Date available: 2009-01-08T17:45:20Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/116982 . Reference: [1] Burke D.K., Hodel R.: The number of compact subsets of a topological space.Proc. Amer. Math. Soc. 58 (1976), 363-368. Zbl 0335.54005, MR 0418014 Reference: [2] Engelking R.: General Topology.Warszawa, 1977. Zbl 0684.54001, MR 0500780 Reference: [3] Ginsburg J., Wood G.: A cardinal inequality for topological space involving closed discrete sets.Proc. Amer. Math. Soc. 64 (1977), 357-360. MR 0461407 .

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