Some stronger forms of topological transitivity and sensitivity for a sequence of uniformly convergent continuous maps

摘要

Let (H, d) be a metric space, F be a Furstenberg family, and (gm)(m is an element of Z+) be a sequence of continuous map on H, which converges uniformly to a map g on H. In this paper, under the condition lim(m ->infinity) d(infinity)(g(m)(m), g(m)) = 0, a necessary and sufficient condition for g to be F-mixing is established. Moreover, let T C Z(+) be an infinite set and