New types of winning strategies via compact spaces

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, Γ*(Ti)-compactness, Γ*(Tj)-compactness, Π*(Ti)-compactness and Π*(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.