Completeness properties of locally quasi-convex groups (Q5929002)

The authors produce samples of metrizable locally quasi-convex groups for which the analogue to the Grothendieck theorem on completeness does not hold. Using the continuous convergence structure on the dual of a topological group, the authors state weaker forms of the Grothendieck theorem valid for all locally quasiconvex groups. Also, they prove that for a smaller class of nuclear groups, BB-reflexivity is equivalent to completeness.