In this appendix we shall record background material on abelian groups. We begin by fixing
standard notation and by listing elementary examples. Basically we stay in the domain of …

Topology is an important and interesting area of mathematics, the study of which will not
only introduce you to new concepts and theorems but also put into context old ones like …

By a character of a group G we mean a homomorphism of G into the group R/Z. If G is an
abelian topological group, the set of all its continuous characters, with addition defined …

The Pontryagin duality theorem for locally compact abelian groups (briefly, LCA groups) has
been the starting point for many different routes of research in Mathematics. From its …

Topologies on the direct sum of topological Abelian groups Page 1 Topology and its
Applications 133 (2003) 209–223 www.elsevier.com/locate/topol Topologies on the direct sum …

It is shown that under mild conditions the path-component of the identity in the dual group $
G\hat\emptyset $ of an Abelian topological group G is precisely the union of the one …

We study a family of idempotent categorical closure operators in the category of topological
Abelian groups (and continuous homomorphisms) related to the von Neumann's kernel. The …

We define a geometry on a group to be an abelian semigroup of symmetric open sets with
certain properties. Examples include well-known structures such as invariant Riemannian …

This paper is a study of certain topological group topologies on the weak or restricted direct
sum of a family of abelian topological groups. Amongst the topologies studied are the …

As shown in [2], closed additive subgroups of nuclear spaces are weakly closed. In other
words, if K is a closed subgroup of a nuclear space E, then the quotient group E/K admits …