Relations Between a Topological Game and the $G_{\delta}$-diagonal property

TL;DR

This paper introduces a new selection principle and a related topological game to characterize the $G_{\delta}$-diagonal property, exploring their interrelations and providing applications and examples.

Contribution

It presents a novel selection principle and a topological game that characterize the $G_{\delta}$-diagonal property, linking game theory with topological properties.

Findings

The selection principle $S_1(\mathcal{O},\mathcal{H})$ characterizes the $G_{\delta}$-diagonal.

The topological game induced by this principle relates to the $G_{\delta}$-property.

Applications and examples illustrate the theoretical results.

Abstract

We present a selection principle $S_1(\mathcal{O},\mathcal{H})$ that characterizes the $G_{\delta}$-diagonal property. We also present a topological game induced by this selection principle and we study the relations between this game and the $G_{\delta}$-property. Finally, we give some applications and examples.