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

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

2008-12-02

arxiv.org/abs/0812.0489v2

Topology and its Applications, 156 (2009), 1216-1223

Mathematics

General Topology

No changes except page layout. 11 pages. To appear in: Topology and its Applications

Scientific paper

10.1016/j.topol.2008.12.009

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.

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