On irresolute multifunctions and related topological games

Abstract

In this paper, we introduce and study α-irresolute multifunctions, and some of their properties are studied. The properties of α-compactness and α-normality under upper α-irresolute multifunctions are topological properties. Also, we prove that the composition of two upper and lower α-irresolute multifunctions is α-irresolute. We apply the results of α-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.

Keywords

• multifunctions
• winning strategy
• topological games
• upper and lower irresolute multifunctions