The strong Pytkeev${}^{\ast }$ property of topological spaces

Abstract

Modifying the known definition of a Pytkeev network, we introduce a notion of Pytkeev${}^{\ast }$ 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${}^{\ast }$ network. In the paper we establish some stability properties of the class of topological spaces with the strong Pytkeev${}^{\ast }$-property.

arXiv comment9 pages. arXiv admin note: text overlap with arXiv:1412.4268