The strong Pytkeev$^*$ property of topological spaces

TL;DR

This paper introduces the Pytkeev$^*$ network concept in topology, establishing its relation to countable Pytkeev networks and analyzing stability properties of spaces with the strong Pytkeev$^*$-property.

Contribution

It defines the Pytkeev$^*$ network, links it to countable Pytkeev networks, and studies stability properties of spaces with the strong Pytkeev$^*$-property.

Findings

A space has a countable Pytkeev network iff it is countably tight and has a countable Pytkeev$^*$ network.

The paper establishes stability properties of spaces with the strong Pytkeev$^*$-property.

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.