Normality and Duality on Topological Groups (Developments in Representation Theory and Related Topics)

Abstract

In this text, we present a result on normality using techniques of duality theory of topological groups. A group topology v on a topological group (G, т) is said to be a compatible topology with the duality (G, GΛ), if the dual groups of G endowed with т and ν coincide, i.e. (G, ν)Λ = (G, т)Λ. The result we show states that for the group G :=ZR, theredo not exist normal locally quasi-convex topologies compatible with the duality (G, GΛ).