# Article

 Title: On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique (English) Author: Ramírez-Páramo, Alejandro Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 46 Issue: 1 Year: 2005 Pages: 131-135 . Category: math . Summary: In this paper we make use of the Pol-Šapirovskii technique to prove three cardinal inequalities. The first two results are due to Fedeli [2] and the third theorem of this paper is a common generalization to: (a) (Arhangel'skii [1]) If $X$ is a $T_{1}$ space such that (i) $L(X)t(X)\leq\kappa$, (ii) $\psi(X)\leq 2^{\kappa}$, and (iii) for all $A \in [X]^{\leq 2^{\kappa}}$, $\left| \overline{A} \right| \leq 2^{\kappa}$, then $|X|\leq 2^\kappa$; and (b) (Fedeli [2]) If $X$ is a $T_2$-space then $|X|\leq 2^{\operatorname{aql}(X)t(X)\psi_c(X)}$. (English) Keyword: cardinal functions Keyword: cardinal inequalities Keyword: Hausdorff space MSC: 54A25 idZBL: Zbl 1121.54013 idMR: MR2175865 . Date available: 2009-05-05T16:50:08Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/119514 . Reference: [1] Arhangel'skii A.V.: The structure and classification of topological spaces and cardinal invariants.Russian Math. Surveys (1978), 33-96. MR 0526012 Reference: [1] Arhangel'skii A.V.: The structure and classification of topological spaces and cardinal invariants.Uspekhi Mat. Nauk 33 (1978), 29-84. MR 0526012 Reference: [2] Fedeli A.: On the cardinality of Hausdorff spaces.Comment. Math. Univ. Carolinae 39.3 (1998), 581-585. Zbl 0962.54001, MR 1666814 Reference: [3] Hodel R.: Cardinal functions I.in: K. Kunen, J. Vaughan (Eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 1-61. Zbl 0559.54003, MR 0776620 Reference: [4] Hodel R.: A technique for proving inequalities in cardinal functions.Topology Proc. 4 (1979), 115-120. MR 0583694 Reference: [5] Juhász I.: Cardinal Functions in Topology - Ten Years Later.Mathematisch Centrum, Amsterdam, 1980. MR 0576927 .

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