Open subgroups, compact subgroups and Binz-Butzmann reflexivity (Q1924649)

The authors investigate the duality of Abelian convergence groups (in the sense of E. Binz and H. Butzmann). It is shown that if an Abelian topological group \(G\) (which in an obvious way is a convergence group) contains an open subgroup \(A\), then \(G\) is convergence reflexive (\(BB\)-reflexive, in the terminology of the present paper) iff \(A\) is \(BB\)-reflexive. Next, if the characters on an Abelian topological group \(G\) separate points and \(K\) is a compact subgroup of \(G\), then \(G\) is \(BB\)-reflexive iff \(G/K\) is \(BB\)-reflexive.