Article

 Title: A remark on the tightness of products (English) Author: Okunev, Oleg Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 37 Issue: 2 Year: 1996 Pages: 397-399 . Category: math . Summary: We observe the existence of a $\sigma$-compact, separable topological group $G$ and a countable topological group $H$ such that the tightness of $G$ is countable, but the tightness of $G\times H$ is equal to $\frak c$. (English) Keyword: tightness Keyword: products Keyword: function spaces MSC: 54A25 MSC: 54B10 idZBL: Zbl 0854.54013 idMR: MR1399012 . Date available: 2009-01-08T18:24:25Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/118842 . Reference: [Arh1] Arhangel'skii A.V.: The frequency spectrum of a topological space and the product operation.Trans. Moscow Math. Soc. 3 (1981), 169-199. Reference: [Arh2] Arhangel'skii A.V.: Topological Spaces of Functions.Kluwer Academic Publishers Dordrecht (1992). Reference: [Kom] Kombarov A.P.: On a strengthening of collectionwise normality.126 Abstracts of the Fifth Tyraspol Symp. on Gen. Topol. and its Appl. (1985), Štiinca Kišinev Russian. Reference: [Law] Lawrence L.B.: Lindelöf spaces concentrated on Bernstein subsets of the real line.Proc. Amer. Math. Soc. (1992), 114 1 211-215. Zbl 0789.54007, MR 1062832 Reference: [OT] Okunev O., Tamano K.: Lindelöf powers and products of function spaces.Proc. Amer. Math. Soc., to appear. Zbl 0858.54013, MR 1353393 Reference: [Mal] Malykhin V.I.: On the tightness and the Suslin number of $\exp X$ and a product of spaces.Soviet. Math. Dokl. (1972), 13 496-499. Reference: [Sha] Shakhmatov D.B.: Compact paces and their generalizations.571-640 Recent Progress in General Topology M. Hušek and J. van Mill North-Holland Amsterdam (1992). MR 1229139 Reference: [Tod] Todorčević S.: Some applications of $S$ and $L$ combinatorics..Annals New York Acad. Sci. 705 (1993), 130-167. MR 1277886 .

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