%0 Journal Article
%T Topological matchings and amenability
%A Friedrich Martin Schneider
%A Andreas Thom
%J Mathematics
%D 2015
%I arXiv
%X 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 uniform coverings. Finally, we prove that the automorphism group of a Fra\"iss\'e limit of a metric Fra\"iss\'e class is amenable if and only if the considered metric Fra\"iss\'e class has a certain Ramsey-type matching property.
%U http://arxiv.org/abs/1502.02293v2