On the Chabauty space of locally compact abelian groups

TL;DR

This paper explores the topological properties of the Chabauty space of locally compact abelian groups, including its dimension, connectedness, and isolated points, providing a comprehensive understanding of its structure.

Contribution

It offers new characterizations of the topological dimension, connectedness, and isolated points in the Chabauty space of locally compact abelian groups.

Findings

Determined the topological dimension of the Chabauty space.

Characterized when the space is totally disconnected or connected.

Identified conditions for isolated points.

Abstract

This paper contains several results about the Chabauty space of a general locally compact abelian group. Notably, we determine its topological dimension, we characterize when it is totally disconnected or connected; we characterize isolated points.