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Topological matchings and amenability

Volume 238 / 2017

Friedrich Martin Schneider, Andreas Thom Fundamenta Mathematicae 238 (2017), 167-200 MSC: Primary 43A07, 28C10; Secondary 22A10, 05D10, 05C55. DOI: 10.4064/fm248-10-2016 Published online: 27 February 2017

Abstract

We establish a characterization of amenability for general Hausdorff 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 Fraïssé limit of a metric Fraïssé class is amenable if and only if the class has a certain Ramsey-type matching property.

Authors

  • Friedrich Martin SchneiderInstitute of Algebra
    TU Dresden
    01062 Dresden, Germany
    e-mail
  • Andreas ThomInstitute of Geometry
    TU Dresden
    01062 Dresden, Germany
    e-mail

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