Arhangelskii's $\alpha$-principles and selection games

TL;DR

This paper explores the properties of Arhangelskii's $eta$-principles, generalizing their characterization via selection principles and analyzing their behavior through selection games.

Contribution

It extends the characterization of Arhangelskii's properties to broader collections and introduces their analysis within the framework of selection games.

Findings

Generalized Arhangelskii's properties for broader collections

Characterization of properties using Scheeper's selection principles

Analysis of these properties through selection games

Abstract

Arhangelskii's properties $\alpha_2$ and $\alpha_4$ defined for convergent sequences may be characterized in terms of Scheeper's selection principles. We generalize these results to hold for more general collections and consider these results in terms of selection games.