No abstract

No abstract

No abstract

Abstract.Let G be a topological Abelian group with character group GA . We will say that G respects compactness if its original topology and the weakest topology that makes each element of GA continuous produce the same compact subspaces. We show the existence of groups which satisfy Pontryagin duality and do not respect compactness, thus furnishing counterexamples to a result published by Venkataraman in 1975. Our counterexamples will be the additive groups of all reflexive infinite-dimensional real Banach spaces. In order to do so, we first characterize those locally convex reflexive real spaces whose additive groups respect compactness. They are exactly the Montel spaces. Finally, we study the class of those groups that satisfy Pontryagin duality and respect compactness.

No abstract