Syndetic proximal set in topological transformation group

Abstract

     In this paper  will study  the syndetic set in topological transformation group. It represents one of the most important sets in topological dynamics that Gottschak referred .We Introduce dynamical  relationship between syndetic set and translation (left-right) ,In topological dynamics group present semi replet set and extensive set .We referred to the relationship of semi replet set and extensive set on the one hand, and their relationship to syndetic set on the other hand . We introduced a new concept syndetic  proximal point that depended on syndetic  set we indicated a relationship syndetic  proximal point  with  proximal point and extensive proximal point , conclude a number of relationships and concepts