Related papers: Property A for coarse spaces

Coarse geometry studies metric spaces on the large scale. The recently introduced notion of coarse entropy is a tool to study dynamics from the coarse point of view. We prove that all isometries of a given metric space have the same coarse…

We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neighborhood property, clearly extends amenability to any locally…

This book offers to study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study "Infinite groups as geometric objects", as Gromov writes it in the title of a famous…

We develop an analog to the ends of a metric space for the category of coarse metric spaces and show that it is equivalent to a previously defined coarse invariant.

There are several characterizations of coarse embeddability of a discrete metric space into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces $L_p(\mu)$, we get…

In this paper we develop the theory of Artin-Wraith glueings for topological spaces. As an application, we show that some categories of compactifications of coarse spaces that agree with the coarse structures are invariant under coarse…

We prove that a metric space with subexponential asymptotic dimension growth has Yu's property A.

The coarse similarity class $[A]$ of $A$ is the set of all $B$ whose symmetric difference with $A$ has asymptotic density 0. There is a natural metric $\delta$ on the space $\mathcal{S}$ of coarse similarity classes defined by letting…

We define a notion of free product for coarse spaces that generalizes the corresponding notion of a free product for groups. We show that free products preserve coarse properties such as coarse property C, finite coarse decomposition…

Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results…

Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…

Sofic groups generalise both residually finite and amenable groups, and the concept is central to many important results and conjectures in measured group theory. We introduce a topological notion of a sofic boundary attached to a given…

A new class of groups, the locally finitely determined groups of local similarities on compact ultrametric spaces, is introduced and it is proved that groups in this class have the Haagerup property (that is, they are a-T-menable in the…

A systolic complex/bridged graph is fit when its (metric) intervals are "not too large". We prove that uniformly locally finite fit systolic complexes have Yu's Property A. In particular, groups acting properly on such complexes have…

For a locally convex $^*$-algebra $A$ equipped with a fixed continuous $^*$-character $\varepsilon$, we define a cohomological property, called property $(FH)$, which is similar to character amenability. Let $C_c(G)$ be the space of…

We explicit Ozawa kernels for classical group theoretical constructions, for discrete metric spaces of finite asymptotic dimension, of large enough Hilbert space compression, and for suitable actions of countable groups on metric spaces. We…

Gromov \cite{Gr$_1$} and Dranishnikov \cite{Dr$_1$} introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we…

A set-theoretic property called Property S is introduced as a generalization of the well-known Property B. Property S is named for A.Schrijver who first used it to formulate an equivalent of the boolean prime ideal theorem. It was…

In this paper we study some basic properties of strong A-statistical convergence and strong A-statistical Cauchyness of sequences in probabilistic metric spaces not done earlier. We also study some basic properties of strong A-statistical…

In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over commutative fields. In the…