Weak covering properties and infinite games

TL;DR

This paper explores game-theoretic aspects of weaker selection principles related to Menger and Rothberger properties, characterizing them through infinite games and using Cohen reals to demonstrate hypothesis necessity.

Contribution

It introduces new game-theoretic characterizations of weaker covering properties and highlights the role of Cohen reals in understanding these principles.

Findings

Certain selection principles are characterized by infinite games.

Cohen reals are used to show the necessity of hypotheses.

New connections between game theory and covering properties are established.

Abstract

We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game. We use generic extensions by Cohen reals to illustrate the necessity of some of the hypotheses in our theorems.