Duality of locally quasi-convex convergence groups

Pranav Sharma

Abstract

In the realm of the convergence spaces, the generalisation of topological groups is the convergence groups, and the corresponding extension of the Pontryagin duality is the continuous duality. We prove that local quasi-convexity is a necessary condition for a convergence group to be c-reflexive. Further, we prove that every character group of a convergence group is locally quasi-convex.


Keywords

continuous duality; convergence groups; local quasi-convexity; Pontryagin duality

Subject classification

54A20; 54H11; 43A40.

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References

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Universitat Politècnica de València

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