@article{Ghanem2022, 
author = {Sewalem Ghanem and Abdelfattah A. El Atik},
title = {On irresolute multifunctions and related topological games},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {10},
pages = {18662-18674},
keywords = {multifunctions, winning strategy, topological games, upper and lower irresolute multifunctions},
url = {https://www.sciopen.com/article/10.3934/math.20221026},
doi = {10.3934/math.20221026},
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.}
}