On irresolute multifunctions and related topological games

AIMS Mathematics

article

Sewalem Ghanem¹  Abdelfattah A. El Atik² 

[1] Department of Mathematics, College of Science and Arts, Qassim University;Department of Mathematics, Faculty of Science, Tanta University

关键词: multifunctions;    winning strategy;    topological games;    upper and lower irresolute multifunctions;   

DOI  :  10.3934/math.20221026

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY