On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique

Ramírez-Páramo, Alejandro. "On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique." Commentationes Mathematicae Universitatis Carolinae 46.1 (2005): 131-135. <http://eudml.org/doc/249542>.

@article{Ramírez2005,
abstract = {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)\le \kappa $, (ii) $\psi (X)\le 2^\{\kappa \}$, and (iii) for all $A \in [X]^\{\le 2^\{\kappa \}\}$, $\left| \overline\{A\} \right| \le 2^\{\kappa \}$, then $|X|\le 2^\kappa $; and (b) (Fedeli [2]) If $X$ is a $T_2$-space then $|X|\le 2^\{\operatorname\{aql\}(X)t(X)\psi _c(X)\}$.},
author = {Ramírez-Páramo, Alejandro},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {cardinal functions; cardinal inequalities; Hausdorff space; cardinal functions; cardinal inequalities},
language = {eng},
number = {1},
pages = {131-135},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique},
url = {http://eudml.org/doc/249542},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Ramírez-Páramo, Alejandro
TI - On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 1
SP - 131
EP - 135
AB - 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)\le \kappa $, (ii) $\psi (X)\le 2^{\kappa }$, and (iii) for all $A \in [X]^{\le 2^{\kappa }}$, $\left| \overline{A} \right| \le 2^{\kappa }$, then $|X|\le 2^\kappa $; and (b) (Fedeli [2]) If $X$ is a $T_2$-space then $|X|\le 2^{\operatorname{aql}(X)t(X)\psi _c(X)}$.
LA - eng
KW - cardinal functions; cardinal inequalities; Hausdorff space; cardinal functions; cardinal inequalities
UR - http://eudml.org/doc/249542
ER -