The Research of the Accessibility and Transitivity of Topological Group

Abstract

The accessibility and transitivity have an important significance in terms of theory and application. The concept of the accessibility and transitivity are introduced in this paper. We study their dynamical properties. The following result are obtained: (l)Let (K , G ) be the hyperspace of (X , G ). Then ( X , G ) is accessible if and only if (K , G ) is accessible; (2) Let (K , G) be the hyperspace of (X , G). Then (X , G ) is transitive if and only if (K , G ) is transitive. These results enriched the theory of the accessibility and transitivity of topological group.