Related papers: The open mapping principle for partial actions of …
Let $X$ be a separable metrizable space. We establish a criteria for the existence of a metrizable globalization for a given continuous partial action of a separable metrizable group $G$ on $X.$ If $G$ and $X$ are Polish spaces, we show…
Given a continuous and isometric action of a Polish group $G$ on an adequate Polish topometric space $(X,\tau,\rho)$ and $x \in X$, we find a necessary and sufficient condition for $\overline{Gx}^\rho$ to be co-meagre; we also obtain a…
We study Borel equivalence relations equipped with a uniformly Borel family of Polish topologies on each equivalence class, and more generally, standard Borel groupoids equipped with such a family of topologies on each connected component.…
We develop the basics of an analogue of descriptive set theory for functions on a Polish space $X$. We use this to define a version of the small index property in the context of Polish topometric groups, and show that Polish topometric…
We give a short proof of an improved version of the Effros Open Mapping Principle via a shift-compactness theorem (also with a short proof), involving `sequential analysis' rather than separability, deducing it from the Baire property in a…
We analyse logic actions of Polish groups which arise in continuous logic. We extend the generalised model theory of H.Becker to the case of Polish G-spaces when G is an arbitrary Polish group.
The first part of these notes give an introduction to the theory of Polish group actions on compact Hausdorff spaces, leading up to a proof of the Kechris-Pestov-Todorcevic correspondence and discussions of properties of universal minimal…
The set of increasing functions on the rational numbers, equipped with the composition operation, naturally forms a topological semigroup with respect to the topology of pointwise convergence in which a sequence of increasing functions…
We define and study Poissonian actions of Polish groups as a framework to Poisson suspensions, characterize them spectrally, and provide a complete characterization of their ergodicity. We further construct 'spatial' Poissonian actions,…
In this work, we give a survey of recent developments in the theory of partial actions of groups and Hopf algebras.
We give strong necessary conditions on the admissibility of a Polish group topology for an arbitrary graph product of groups $G(\Gamma, G_a)$, and use them to give a characterization modulo a finite set of nodes. As a corollary, we give a…
In this paper we investigate the action of Polish groups (not necessary abelian) on an uncountable Polish spaces. We consider two main situations. First, when the orbits given by group action are small and the second when the family of…
A Polish group is surjectively universal if it can be continuously homomorphically mapped onto every Polish group. Making use of a type of new metrics on free groups \cite{DG}, we prove the existence of surjectively universal Polish groups,…
We establish a characterization of extreme amenability of any Polish group in Fra\"iss\'e-theoretic terms in the setting of continuous logic, mirroring a theorem due to Kechris, Pestov and Todorcevic for closed subgroups of the permutation…
We associate to every action of a Polish group on a standard probability space a Polish group that we call the orbit full group. For discrete groups, we recover the well-known full groups of pmp equivalence relations equipped with the…
We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…
We define some coding of Borel sets in admissible sets. Using this we generalize certain results from model theory involving admissible sets to the case of continuous actions of closed permutation groups on Polish spaces. In particular we…
We study continuous actions of Polish groups on Polish spaces. We develop Scott analysis introduced by Hjorth for studying orbit equivalence relations. We define eventually open actions and prove that this property characterizes the actions…
We extend the Becker--Kechris topological realization and change-of-topology theorems for Polish group actions in several directions. For Polish group actions, we prove a single result that implies the original Becker--Kechris theorems, as…
We show that the enveloping space $X_G$ of a partial action of a Polish group $G$ on a Polish space $X$ is a standard Borel space, that is to say, there is a topology $\tau$ on $X_G$ such that $(X_G, \tau)$ is Polish and the quotient Borel…