Topological matchings and amenability

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

We establish a characterization of amenability for general Hausdor topological groups in terms of matchings with respect to finite uniform coverings. Furthermore, we prove that it suffices to just consider two-element uniform coverings. We also show that extremely amenable as well as compactly approximable topological groups satisfy a perfect matching property condition-the latter even with regard to arbitrary (i.e., possibly infinite) uniform coverings. Finally, we prove that the automorphism group of a Fraisse limit of a metric Fraisse class is amenable if and only if the class has a certain Ramsey-type matching property.

Details

Original languageEnglish
Pages (from-to)167-200
Number of pages34
JournalFundamenta Mathematicae
Volume238
Issue number2
Publication statusPublished - 2017
Peer-reviewedYes

External IDs

ORCID /0000-0002-7245-2861/work/173049655

Keywords

ASJC Scopus subject areas

Keywords

  • Continuous logic, Invariant means, Matchings in bipartite graphs, Ramsey theory, Topological groups