Jayne and Rogers introduced the notion of fragmentability in 1983, proving several facts about usco maps on spaces with the property. Like many useful topological properties, fragmentability can be characterized in terms of the existence of a winning strategy for the second player in a topological game.
After a brief overview of fragmentable spaces, we will examine a game used by Michael to characterize complete metrizability, and a modification of it used by Kenderov and Moors to characterize fragmentability.
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