Polish topometric groups

This property, which is a particular instance of a very general notion due to Malcev, was introduced and studied in the group-theoretic setting by Gordon- Vershik [GV97] and St¨

We show that any Polish group with ample generics embeds into a connected Polish group with ample generics and that full groups of type III hyperfinite ergodic equivalence

We conclude with a general characterisation/classification of transitive continuous isometric actions of a Roeckle-precompact Polish groups on a complete metric spaces?. In

It was shown by Uspenskij [Usp90] that the isometry group of the Urysohn space U is a universal Polish group, namely, that any other Polish group is homeomorphic to a

When X = G and the action is given by group multiplication, functions might also be left uniformly continuous, and if they are simultaneously in RUC(G) they form part of the

We use this to define a version of the small index property in the context of Polish topometric groups, and show that Polish topometric groups with ample generics have this

Inspired by those results, Kechris, Pestov, and Todorcevic [KPT], using the general framework of Fraïssé limits, for- mulated a precise correspondence between the structural

It turns out that the answer to the Question 1.3 is “very much negative”, so to speak, that is: apart from the exceptional case of two dimensional hyperbolic orbifolds, in the