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Dual Selection Games by Clontz, Steven is a scholarly article available to read on EtoBox.

What is Dual Selection Games about?

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 $\{\operatorname{ran}{f}:f\in\mathbf C(\mathcal R)\}$ is coinitial in $\mathcal A$ with respect to $\subseteq$, where $\mathbf C(\mathcal R)=\{f\in(\bigcup\mathcal R)^{\mathcal R}:R\in\mathcal R\Rightarrow f(R)\in R\}$ collects the choice functions on the set $\mathcal R$, then $G_1(\mathcal A,\mathcal B)$ and $G_1(\mathcal R,\neg\mathcal B)$ are dual selection games.

Author

Clontz, Steven

Published

2018

Language

EN