On F{\o}lner sets in topological groups
Group Theory
2019-02-20 v2 Functional Analysis
General Topology
Abstract
We extend F{\o}lner's amenability criterion to the realm of general topological groups. Building on this, we show that a topological group is amenable if and only if its left translation action can be approximated in a uniform manner by amenable actions on the set . As applications we obtain a topological version of Whyte's geometric solution to the von Neumann problem and provide an affirmative answer to a question posed by Rosendal.
Cite
@article{arxiv.1608.08185,
title = {On F{\o}lner sets in topological groups},
author = {Friedrich Martin Schneider and Andreas Thom},
journal= {arXiv preprint arXiv:1608.08185},
year = {2019}
}
Comments
34 pages, no figures. v2: We added Corollary 4.8 as well as an example of an amenable Polish group which is not F{\o}lner amenable in the sense in Rosendal