令X为紧致度量空间,f:X→X为连续映射,U,V为X的任意非空开集,若{n>0|fn(U)∩V≠ )为正上密度集,则称f拓扑遍历.f拓扑双重遍历意味着f×f拓扑遍历.本文在[2]的基础上进一步讨论拓扑遍历与拓扑双重遍历映射的性质.

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.