Building suitable sets for locally compact groups by means of continuous selections
arXiv:0812.0489 · doi:10.1016/j.topol.2008.12.009
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.
No changes except page layout. 11 pages. To appear in: Topology and its Applications