
TL;DR
This paper explores the concept of duality in selection games, establishing a general theorem that relates winning strategies in dual pairs of such games through coinitiality conditions.
Contribution
It introduces a broad theorem linking dual selection games via coinitiality, extending known dualities like the Rothberger and point-open games.
Findings
Established a general duality theorem for selection games.
Connected specific examples like Rothberger and point-open games.
Provided conditions under which strategies in dual games correspond.
Abstract
Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strategy for the opponent in the dual. For example, the Rothberger selection game involving open covers is dual to the point-open game. This extends to a general theorem: if is coinitial in with respect to , where collects the choice functions on the set , then and are dual selection games.
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