Some consequences of an easy cardinal inequality involving separating open covers

Abstract

Vengono fornite alcune disuguaglianze cardinali relative a varie funzioni cardinali definite in termini di certi ricoprimenti aperti. Tra l'altro si prova che $\mid X\mid\leq e(X)^{\psi m(X)}$ e $\mid X\mid\leq wL(X)^{\psi u(X)}$ per ogni T$_{1}$-spazio x completamente regolare. Qui e (X), wL(X), $\psi m(X)$ e $\psi u(X)$ denotano rispettivamente l'estensione, il numero debole di Lindel$\ddot{\textrm{o}}$f.

Some cardinal inequalities with cardinal functions defined in terms of certain typed of covers are given. Among other results it is shown that $\mid X\mid\leq e(X)^{\psi m(X)}$ and $\mid X\mid\leq wL(X)^{\psi u(X)}$ for any completely regular T$_{1}$-space x. Here e (X), wL(X), $\psi m(X)$ e $\psi u(X)$ denote respectively the extent, the weak Lindel$\ddot{\textrm{o}}$f number, the pseudo-metrizability degree and the pseudo uniform weight of X.