Abstract
Current paper aims to introduce new types of compactness in terms of notion of K-cover in topological games with perfect information of Telgarsky,namely, Γ*(Ti)-compactness, Γ*(Tj)-compactness, Π*(Ti)-compactness and Π*(Tj)-compactness in the realm of Hausdorff 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.
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