Some topological properties of topological rough groups

Let (U, R) be an approximation space with U being non-empty set and R equivalence relation on U, let $${\overline{G}}$$ $${\underline{G}}$$ the upper lower of subset G U. A topological rough group is a $$G=({\underline{G}}, {\overline{G}})$$ endowed topology, which induced from , such that product mapping $$f: G\times G\rightarrow {\overline{G}}$$ inverse are continuous. In class groups, relations some separation axioms obtained; basic properties neighborhoods identity element subgroups investigated. particular, examples groups provided to clarify facts about groups. Moreover, version open theorem in obtained. Further, interesting questions posed.