Related papers: Sequential ends of metric spaces
This note extends the invariant defined in "An invariant of metric spaces under bornologous equivalences" to the coarse category.
This paper presents a new version of boundary on coarse spaces. The space of ends functor maps coarse metric spaces to uniform topological spaces and coarse maps to uniformly continuous maps.
"An invariant of metric spaces under bornologous equivalences" gives an invariant and "A coarse invariant" extends the invariant to coarse equivalences. In both papers the invariant is defined for a class of metric spaces called sigma…
Inspired by group cohomology, we define several coarse topological invariants of metric spaces. We define the coarse cohomological dimension of a metric space, and demonstrate that if G is a countable group, then the coarse cohomological…
We introduce a notion of equivariant coarse cohomology of the complement of a subspace in a metric space. We use this cohomology to define a notion of coarse cohomology of the configuration space of a metric space and develop tools to…
We classify the metric spaces that can be approximated by finite homogeneous ones.
We define coarse proximity structures, which are an analog of small-scale proximity spaces in the large-scale context. We show that metric spaces induce coarse proximity structures, and we construct a natural small-scale proximity…
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…
Using the category of metric spaces as a template, we develop a metric analogue of the categorical semantics of classical/intuitionistic logic, and show that the natural notion of predicate in this "continuous semantics" is equivalent to…
In this paper we define the coarse (co)homology of the complement of a subspace in a metric space, generalizing the coarse (co)homology of Roe. We give a model space which encodes coarse geometric structure of the complement. We also…
A new sequential approach to investigations of structure of metric spaces at infinity is proposed. Criteria for finiteness and boundedness of metric spaces at infinity are found.
Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…
We define a class of trim metric spaces and show that every finite metric space is the leaf space of a metric forest with trim base.
In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…
In this article, the author proposes another way to define the completion of a metric space, which is different from the classical one via the dense property, and prove the equivalence between two definitions. This definition is based on…
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…
In this paper we introduce the notions of statistical convergence and statistical Cauchyness of sequences in a metric-like space. We study some basic properties of these notions
A class $\mathfrak{M}$ of coarse spaces is called a variety if $\mathfrak{M}$ is closed under formation of subspaces, coarse images and products. We classify the varieties of coarse spaces and, in particular, show that if a variety…
A metric algebra is a metric variant of the notion of $\Sigma$-algebra, first introduced in universal algebra to deal with algebras equipped with metric structures such as normed vector spaces. In this paper, we showed metric versions of…
Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a…