Show that if a group G acts freely and properly discontinuously on a Hausdorff space X, then the action is a covering space action. (Here 'properly discontinuously' means that each x∈X has a neighborhood U such that {g∈G∣U∩g(U)=∅} is finite.) In particular, a free action of a finite group on a Hausdorff space is a covering space action.