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arXiv · 2110.07030

On strategies for selection games related to countable dimension

Christopher Caruvana·Steven Clontz
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Abstract

Two selection games from the literature, $G_c(\mathcal O,\mathcal O)$ and $G_1(\mathcal O_{zd},\mathcal O)$, are known to characterize countable dimension among certain spaces. This paper studies their perfect- and limited-information strategies, and investigates issues related to non-equivalent characterizations of zero-dimensionality for spaces that are not both separable and metrizable. To relate results on zero-dimensional and finite-dimensional spaces, a generalization of Telgársky's proof that the point-open and finite-open games are equivalent is demonstrated.

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Christopher Caruvana, Steven Clontz. 2021-10-13. On strategies for selection games related to countable dimension. https://doi.org/10.2298/fil2219503c

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