On strategies for selection games related to countable dimension

Abstract

Two selection games from the literature,
\(G_c(\mc O,\mc O)\) and \(G_1(\mc O_{zd},\mc O)\),
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 Telg\'{a}rsky's
proof that the point-open and finite-open games
are equivalent is demonstrated.