Expansive Behaviours for Homeomorphisms of tvs-Cone Metric Spaces

Let f be a homeomorphism of a compact tvs-cone metric space. In this paper,we show that f is tvs-cone expansive if and only if f has a generator. Further, it is proved that if f is tvs-cone expansive, then the set of points having converging semiorbits under f is a countable set. Results of this paper improve some expansive homeomorphisms theorems in topological dynamics, which will help to research dynamical properties for homeomorphisms of tvs-cone metric spaces.