On strategies for selection games related to countable dimension


Christopher Caruvana, Steven Clontz




Two selection games from the literature, G c (O, O) and G 1 (O zd , 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.