On g-barrelled groups and their permanence properties

Abstract

The g -barrelled groups constitute a vast class of abelian topological groups. It might be considered as a natural extension of the class of barrelled topological vector spaces. In this paper we prove that g -barrelledness is a multiplicative property, thus we obtain new examples of g -barrelled groups. We also prove that direct sums and inductive limits of g -barrelled locally quasi-convex groups are g -barrelled, too. Other permanence properties are considered as well.