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On Følner sets in topological groups

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.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:70711
Date04 June 2020
CreatorsSchneider, Friedrich Martin, Thom, Andreas
PublisherCambridge University Press
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess
Relation0010-437X, 1570-5846, 10.1112/S0010437X1800708X, info:eu-repo/grantAgreement/European Research Council/European Union’s Seventh Framework Programme/277728//FP7/2007-2013

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