On Geometric Space and Its Applications in Topological H_v -groups

Abstract

We generalize the concept of topological hypergroup to topological Hv-group and defifine some topologies on Hv-groups by using the concept of geometric space, which was defifined by Freni. By applying these topologies, we have always a topological Hv-group without need any more conditions. Moreover, we state some conditions on a topological Hv-group that make it complete.