On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique

Ramírez-Páramo, Alejandro

Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 1, pp. 131-135.

Résumé

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 $|X|\leq 2^{\operatorname{aql}(X)t(X)\psi_c(X)}$.

Détail

Classification : 54A25
Keywords: cardinal functions; cardinal inequalities; Hausdorff space