A closed subgroup $H$ of a locally compact group $G$ is confined if the closure conjugacy class in Chabauty space does not contain trivial subgroup. We establish dynamical criterion on action totally disconnected $X$ ensuring that no relatively amenable can be confined. This property equivalent to fact its Furstenberg boundary free. Our applies Neretin groups. deduce each has two inequivalent i...

Let G be a locally compact amenable group, TLIM ( ) the topological left-invariant means on , and 0 limit points of Følner-nets. I show that = unless is σ -compact non-unimodular, in which case ≠ . This improves 1970 result Chou 2009 Hindman Strauss. consider analogous problem for non-topological means, give short construction net converging to invariance “weakly but not strongly,” simplifying ...

We demonstrate that the perforative phenomena shown to occur among simple amenable C∗-algebras by Villadsen and Toms can be realized within a dynamical framework. More specifically, we construct a minimal homeomorphism for which the K0 group of the crossed product fails to be weakly unperforated, and a minimal homeomorphism for which the crossed product has the same Elliott invariant as an AT-a...

We study the definable topological dynamics (G(M),SG(M)) of a group acting on its type space, where M is either an o-minimal structure or p-adically closed field, and G definably amenable group. focus problem raised in [13] whether weakly generic types coincide with almost periodic types, showing that answer positive when has boundedly many global types. also give two “minimal counterexamples” ...

in this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric connes amenability. we determine symmetric module amenability and symmetric connes amenability of some concrete banach algebras. indeed, it is shown that $ell^1(s)$ is  a symmetric $ell^1(e)$-module amenable if and only if $s$ is amenable, where $s$ is an inverse semigroup with subsemigr...