Locally quasi-convex convergence groups

Duality of locally quasi-convex convergence groups

“…For details regarding the continuous duality for convergence groups refer [4,6]. Further, the notion of locally quasi-convex convergence groups is introduced in [12]. Here, we prove that local quasi-convexity is a necessary condition for a convergence group to be c-reflexive, and then we prove that every character group of a convergence group is locally quasi-convex.…”

“…Therefore, the analog of Pontryagin duality theorem, valid in the context of abelian topological groups, cannot be directly extended to abelian convergence groups. Motivated from the notion of local quasi-convexity [2] in topological groups, the notion of local quasi-convexity for convergence groups is defined in [12].…”