This paper initiates the formal study of those classes of locally convex spaces which are
closed under the taking of arbitrary subspaces, separated quotients, cartesian products and …

This paper aims to study the dual of an extended locally convex space. In particular, we
study the weak and weak⁎ topologies for an extended locally convex space and give …

1. Varieties of groups. The study of varieties of groups (more generally, varieties of algebras)
has its roots in the work of Birkhoff [4] and Neumann [60] in the 1930's. A variety of groups …

Recently several papers on varieties of topological groups have appeared. In this note we
investigate the question: if Ω is a class of topological groups, what topological groups are in …

The concept of approximating in various ways locally compact groups by Lie groups is
surveyed with emphasis on pro-Lie groups and locally compact residual Lie groups. All …

A pro-Lie group is a projective limit of a projective system of finite dimensional Lie groups. A
prodiscrete group is a complete abelian topological group in which the open normal …

Recently several papers on varieties of topological groups and varieties of locally convex
spaces have appeared.(We include a somewhat complete bibliography.) This paper …

Let E be any metrizable nuclear locally convex space and E^ the Pontryagin dual group of E.
Then the topological group E^ has the tubby torus (that is, the countably infinite product of …