Abstract
<abstract><p>In this paper, we introduce and study $ \alpha $-irresolute multifunctions, and some of their properties are studied. The properties of $ \alpha $-compactness and $ \alpha $-normality under upper $ \alpha $-irresolute multifunctions are topological properties. Also, we prove that the composition of two upper and lower $ \alpha $-irresolute multifunctions is $ \alpha $-irresolute. We apply the results of $ \alpha $-irresolute multifunctions to topological games. Upper and lower topological games are introduced. The set of places for player ONE in upper topological games may guarantee a gain is semi-closed. Finally, some optimal strategies for topological games are defined and studied.</p></abstract>
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