New types of winning strategies via compact spaces

Abstract

Current paper aims to introduce new types of compactness in terms of notion of K-cover in topological games with perfect information of Telgársky,namely, ∗(Ti)-compactness, ∗(Tj)-compactness, ∗(Ti)-
compactness and ∗(Tj)-compactness in the realm of Hausdörff spaces. We give a necessary and sufficient
condition for players to have a winning strategy in these types of compactness. Furthermore, various
characterizations of these concepts are achieved