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On Følner sets in topological groups
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 7 / July 2018
- Published online by Cambridge University Press:
- 16 May 2018, pp. 1333-1361
- Print publication:
- July 2018
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- Article
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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 give an affirmative answer to a question posed by Rosendal.
