Isometrisable group actions

Itaï Ben Yaacov (1) , Julien Melleray (1)

1 AGL - Algèbre, géométrie, logique

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.

Mots clés: Polish space; isometry; group action

Domaines: Logique [math.LO]; Systèmes dynamiques [math.DS]

Itaï Ben Yaacov, Julien Melleray. Isometrisable group actions. Proceedings of the American Mathematical Society, 2016, 144 (9), pp.4081--4088. ⟨hal-01016439v2⟩