Infinite Games Associated with Asymmetric Topology and Applications

Jiling Cao


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.

Quasi-metric, dual, $kappa$-semi-stratifiable, game-compact, multi-valued map.

Math Review Classification
Primary 54C60, 54E20 ; Secondary 54E15, 90D44

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17 pages

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