Isometrisable group actions

Itaï Ben Yaacov, Julien Melleray

Published 2014-06-30, updated 2015-11-27Version 2

Given a separable metrisable space X, and a group G of homeomorphisms of X, we introduce a topological property of the action of G on X which is equivalent to the existence of a G-invariant compatible metric on X. This extends a result of Marjanovic obtained under the additional assumption that X is locally compact.