Some classes of minimally almost periodic topological groups

TL;DR

This paper introduces classes of topological groups called SSGP(n), explores their hierarchical relationships, and examines their properties, revealing their presence in many known examples of abelian minimally almost periodic groups.

Contribution

The paper defines new classes of topological groups, establishes their inclusions, and investigates their properties, connecting them to existing examples in the literature.

Findings

SSGP(n) classes are properly contained within m.a.p. groups.

Properties like products and quotients are studied within these classes.

Many early examples of abelian m.a.p. groups exhibit SSGP(1) or SSGP(2) properties.

Abstract

Classes SSGP(n)(n < \omega) of topological groups are defined, and the class-theoretic inclusions SSGP(n) \subseteq SSGP(n+1) \subseteq m.a.p. are established and shown proper. These classes are investigated with respect to the properties normally studied by topologists (products, quotients, passage to dense subgroups, and the like). In passing the authors establish the presence of the SSGP(1) or SSGP(2) property in many of the early examples in the literature of abelian m.a.p. groups.