Consonant spaces and topological games

Abstract

We establish and investigate a connection between the subject areas of topological games and consonant spaces. In particular, we show that a subspace A of a compact metric space is consonant exactly when its complement B has the property that Player One has no winning strategy in the topological game where Player One plays an open k-cover of B and Player Two picks an element of the k-cover in each round. Here Player One wins when the choices of Player Two fail to cover B.