Building suitable sets for locally compact groups by means of continuous selections

TL;DR

This paper provides a new, purely topological proof for the existence of suitable sets in locally compact groups, utilizing Michael's selection theorem and elementary group theory.

Contribution

It introduces a self-contained, topological approach to establishing the existence of suitable sets in locally compact groups, simplifying previous proofs.

Findings

Existence of suitable sets in locally compact groups confirmed

Application of Michael's selection theorem in group theory

Elementary topological methods used for proof

Abstract

If a discrete subset S of a topological group G with the identity 1 generates a dense subgroup of G and S \cup {1} is closed in G, then S is called a suitable set for G. We apply Michael's selection theorem to offer a direct, self-contained, purely topological proof of the result of Hofmann and Morris on the existence of suitable sets in locally compact groups. Our approach uses only elementary facts from (topological) group theory.