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

Dmitri Shakhmatov

Published 2008-12-02, updated 2008-12-04Version 2

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.