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 …

This is a survey on the recent progress in minimal topological groups, with a particular
emphasis on constructions leading to non-abelian minimal groups, as semidirect products …

Two non-discrete T1 topologies τ1, τ2 on a set X are called independent if their intersection
τ1∩ τ2 is the cofinite topology on X. We show that a countable group does not admit a pair …

A subset S of a topological group G is said to be a suitable set if (a) it has the discrete
topology,(b) it is a closed subset of G {1}, and (c) the subgroup generated by S is dense in …

We continue the work initiated in our earlier article (J. Pure Appl. Algebra 70 (1991) 53–72);
as there, for G a group let B (G)(respectively N (G)) be the set of Hausdorff group topologies …

GENERATING SETS FOR COMPACT SEMISIMPLE LIE GROUPS 1. Introduction Suppose that Γ
is a compact connected Lie group of dimension Page 1 PROCEEDINGS OF THE AMERICAN …

We introduce and study the model-theoretic notions of absolute connectedness and type-
absolute connectedness for groups. We prove that groups of rational points of split …

We discuss the structure and Cartesian products of the countably compact groups G that
satisfy the following forms of the open mapping theorem:(a) every continuous surjective …

If a discrete subset S of a topological group G with identity 1 generates a dense subgroup of
G and S∪{1} is closed in G, then S is called a suitable set for G. We construct in ZFC a …

A discrete subset S of a topological group G with identity 1 is called suitable for G if S
generates a dense subgroup of G and S∪{1} is closed in G. We study various algebraic and …