Open subgroups and Pontryagin duality
An abelian topological group is called reflexive if the evaluation map \(G\to G\widehat{\phantom{x}}\widehat{\phantom{x}}\) is a topological isomorphism of \(G\) onto its second character group. We say that \(G\) is strongly reflexive if all closed subgroups and Hausdorff quotient groups of \(G\) and of \(G\widehat{\phantom{x}}\) are reflexive. Let \(A\) be an open subgroup of \(G\); it is proved that \(G\) is reflexive (resp. strongly reflexive) if and only if \(A\) is reflexive (resp. strongly reflexive).
scientific article; zbMATH DE number 567397