Dual Selection Games

2018/09/27 by Clontz, Steven · 1 citation
#54D20 #54D45 #91A44 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1809.10783

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 \ranf:f∈\mathbf C(\mathcal R)\ is coinitial in \mathcal A with respect to ⊆, where \mathbf C(\mathcal R)=\f∈(\bigcup\mathcal R)^{\mathcal R}:R∈\mathcal R⇒ f(R)∈ R\ collects the choice functions on the set \mathcal R, then G₁(\mathcal A,\mathcal B) and G₁(\mathcal R,¬\mathcal B) are dual selection games.

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