Selective game version of q-points

TL;DR

This paper introduces a new selection principle and topological game to characterize q-points and explores their relationships with other topological concepts and games.

Contribution

It presents the selection principle $S_1^*( au_x,CD)$ for characterizing q-points and analyzes the associated topological game $G_1^*( au_x,CD)$ and its connections.

Findings

Characterization of q-points via the selection principle.

Analysis of the game $G_1^*( au_x,CD)$ and its relation to W-points.

Connections established between different topological games.

Abstract

This work presents the selection principle $S_1^*(\tau_x,CD)$ that characterizes $q$-points. We also discuss the induced topological game $G_1^*(\tau_x,CD)$ and its relations with $W$-points and $\widetilde{W}$-points, as well as with the game $G_1(\Omega_x,\Omega_x)$.