On strategies for selection games related to countable dimension

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.