Topological matchings and amenability

Friedrich Martin Schneider ¹   ; Andreas Thom ²

¹ Institute of Algebra TU Dresden 01062 Dresden, Germany
² Institute of Geometry TU Dresden 01062 Dresden, Germany

Fundamenta Mathematicae, Tome 238 (2017) no. 2, pp. 167-200

Résumé

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.

Détail

DOI : 10.4064/fm248-10-2016

Keywords: establish characterization amenability general hausdorff topological groups terms matchings respect finite uniform coverings furthermore prove suffices just consider two element uniform coverings extremely amenable compactly approximable topological groups satisfy perfect matching property condition latter even regard arbitrary possibly infinite uniform coverings finally prove automorphism group fra limit metric fra class amenable only class has certain ramsey type matching property