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

Dmitri Shakhmatov

doi:10.1016/j.topol.2008.12.009

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arXiv · 0812.0489

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

Dmitri Shakhmatov

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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.

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Dmitri Shakhmatov. 2008-12-04. Building suitable sets for locally compact groups by means of continuous selections. https://doi.org/10.1016/j.topol.2008.12.009

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