Let X be a compact metric space and f : X →X a continuous onto map. f is called topologically ergodic if for any nonempty open sets U, V of X, {n > O | fn(U)∪ V ≠} is a set of positive upper density. Topological double ergodicity means that f@f is topologically ergodic. In this paper, we shall use the results in [2] to study the properties of topologically ergodic maps and topologically double ergodic maps.
