Abstract:In this paper we make use of the Pol-\v Sapirovskii 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 $|X|\leq 2^{aql(X)t(X)\psi _c(X)}$.
Keywords: cardinal functions, cardinal inequalities, Hausdorff space
AMS Subject Classification: 54A25