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arXiv · 1608.08185

On F{\o}lner sets in topological groups

Friedrich Martin Schneider·Andreas Thom
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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 $G$ is amenable if and only if its left translation action can be approximated in a uniform manner by amenable actions on the set $G$. 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.

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Friedrich Martin Schneider, Andreas Thom. 2016-08-29. On F{\o}lner sets in topological groups. https://doi.org/10.1112/s0010437x1800708x

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