Topological matchings and amenability
Research output: Contribution to journal › Research article › Contributed › peer-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 language | English |
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Pages (from-to) | 167-200 |
Number of pages | 34 |
Journal | Fundamenta Mathematicae |
Volume | 238 |
Issue number | 2 |
Publication status | Published - 2017 |
Peer-reviewed | Yes |
External IDs
ORCID | /0000-0002-7245-2861/work/173049655 |
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Keywords
ASJC Scopus subject areas
Keywords
- Continuous logic, Invariant means, Matchings in bipartite graphs, Ramsey theory, Topological groups