The strong Pytkeev$^*$ property of topological spaces

Abstract

Modifying the known definition of a Pytkeev network, we introduce a notion of Pytkeev$^*$ network and prove that a topological space has a countable Pytkeev network if and only if $X$ is countably tight and has a countable Pykeev$^*$ network. In the paper we establish some stability properties of the class of topological spaces with the strong Pytkeev$^*$-property.