| In this paper, we study two types of topological games, ${cal G}(x)$-games and ${cal G}({cal F})$-games, and topological spaces defined by them, namely $cal G$-spaces and game-compact spaces. It is shown these games are associated with $kappa$-semi-stratifiabilty, which is the duality of quasi-metrizability. Finally, we apply these games and relevant properties to study multi-valued maps. Consequently, the Choquet-Dolecki theorem on multi-valued maps is deduced. Main results of Hansell et al in cite{Ha} are generalized. |
Keywords
Quasi-metric, dual, $kappa$-semi-stratifiable, game-compact, multi-valued map.
Math Review Classification
Primary 54C60, 54E20
; Secondary 54E15, 90D44
Last Updated
Length
17 pages
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