On geometric space and its applications in topological Hv-groups

We generalize the concept of topological hypergroup to topological Hv-group and define some topologies on Hv-groups by using the concept of geometric space, which was defined 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. Our aim is to generalize the concept of topological hypergroup to topological Hv-group via considering the characteristics of the induced geometric space.