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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:70711 |
| Date | 04 June 2020 |
| Creators | Schneider, Friedrich Martin, Thom, Andreas |
| Publisher | Cambridge University Press |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 0010-437X, 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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