New criteria for equivalence of locally compact abelian groups

TL;DR

This paper establishes new criteria for when two locally compact abelian groups are topologically isomorphic based on the isometry of open subgroups of their measure groups.

Contribution

It introduces novel criteria linking isometric open subgroups of measure groups to the topological isomorphism of the underlying LCA groups.

Findings

Open subgroup isometry implies topological isomorphism of LCA groups

New criteria for group equivalence based on measure group isometries

Advances understanding of measure group structures in LCA groups

Abstract

If an open subgroup of the group of the invertible measures on a LCA group is isometric to another, then the correspoinding underlying LCA groups are topologically isomorphic to each other.