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

2022/04/09 by Saak Gabriyelyan, Gabriyelyan, Saak
Mathematics · #46A8 #46E10 #54H11 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2204.04389

openalex publication_date 2022/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a locally quasi-convex (lqc) abelian group G, we give the first description of all compatible group topologies on G 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.

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