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

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.