Amenability and Ramsey theory in the metric setting
Volume 231 / 2015
Fundamenta Mathematicae 231 (2015), 19-38
MSC: Primary 37B05; Secondary 05D10, 03C90, 03C52, 03E15.
DOI: 10.4064/fm231-1-2
Abstract
Moore [Fund. Math. 220 (2013)] characterizes the amenability of the automorphism groups of countable ultrahomogeneous structures by a Ramsey-type property. We extend this result to the automorphism groups of metric Fraïssé structures, which encompass all Polish groups. As an application, we prove that amenability is a $G_\delta $ condition.
