We generalize the concept of topological hypergroup to topological H v-group and define some topologies on H ᵥ-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 H v-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