On Følner sets in topological groups

Abstract

We extend Følner'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.

34 pages, no figures. v2: We added Corollary 4.8 as well as an example of an amenable Polish group which is not Følner amenable in the sense in Rosendal

References in corpus (4)

• Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces
• Baire measurable paradoxical decompositions via matchings
• Topological matchings and amenability
• Continuity of convolution and SIN groups

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