Extremal k-pseudocompact abelian groups

TL;DR

This paper generalizes previous results on pseudocompact abelian groups, showing that for certain weights, such groups contain proper dense subgroups and can have finer pseudocompact topologies.

Contribution

It extends the understanding of k-pseudocompact abelian groups by establishing the existence of proper dense subgroups and the possibility of refining their topologies.

Findings

Existence of proper dense k-pseudocompact subgroups in groups of weight >k

Groups admit strictly finer k-pseudocompact topologies

Generalization of previous results by Comfort and van Mill

Abstract

For a cardinal k, generalizing a recent result of Comfort and van Mill, we prove that every k-pseudocompact abelian group of weight >k has some proper dense k-pseudocompact subgroup and admits some strictly finer k-pseudocompact group topology.