ALGEBRAIC STRUCTURE OF ABELIAN GROUPS INDUCED BY CONTINUOUS HOMOMORPHIC IMAGES TO COMPACT GROUPS (Recent Progress in General Topology and its Related Fields)

Abstract

As usual, ℤ and ℕ denote the integer and natural numbers respectively, we also let ℕ⁺ = ℕ {0}. Given a group we shall denote by ℯ its neutral element. We say that a group G is torsion if every element of G is of finite order. A group G is bounded if there exists a positive integer n satisfying gⁿ = ℯ for every g ∈ G. We shall use the bold letters P and Q to denote properties of topological groups. Finally, all topological groups are assumed to be Hausdorff.