English

Compatible group topologies on a locally quasi-convex abelian group and the Mackey group problem

Group Theory 2022-04-12 v1 General Topology

Abstract

For a locally quasi-convex (lqc) abelian group GG, we give the first description of all compatible group topologies on GG and apply this result to the Mackey group problem for lqc groups. We characterize lqc abelian groups which are Mackey groups or admit a Mackey group topology and provide a characterization of two Mackey groups whose product is Mackey. We obtain the first characterization of locally convex spaces which are Mackey groups.

Keywords

Cite

@article{arxiv.2204.04389,
  title  = {Compatible group topologies on a locally quasi-convex abelian group and the Mackey group problem},
  author = {Saak Gabriyelyan},
  journal= {arXiv preprint arXiv:2204.04389},
  year   = {2022}
}