On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 1, pp. 131-135
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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 $|X|\leq 2^{\operatorname{aql}(X)t(X)\psi_c(X)}$.
@article{CMUC_2005__46_1_a11,
author = {Ram{\'\i}rez-P\'aramo, Alejandro},
title = {On the cardinality of {Hausdorff} spaces and {Pol-\v{S}apirovskii} technique},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {131--135},
publisher = {mathdoc},
volume = {46},
number = {1},
year = {2005},
mrnumber = {2175865},
zbl = {1121.54013},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2005__46_1_a11/}
}
TY - JOUR AU - Ramírez-Páramo, Alejandro TI - On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique JO - Commentationes Mathematicae Universitatis Carolinae PY - 2005 SP - 131 EP - 135 VL - 46 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CMUC_2005__46_1_a11/ LA - en ID - CMUC_2005__46_1_a11 ER -
%0 Journal Article %A Ramírez-Páramo, Alejandro %T On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique %J Commentationes Mathematicae Universitatis Carolinae %D 2005 %P 131-135 %V 46 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/CMUC_2005__46_1_a11/ %G en %F CMUC_2005__46_1_a11
Ramírez-Páramo, Alejandro. On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 1, pp. 131-135. http://geodesic.mathdoc.fr/item/CMUC_2005__46_1_a11/