Related papers: A totally bounded Uniformity on coarse metric Spac…
To a metric space $X$ we associate a compact topological space $\nu' X$ called the corona of $X$. Then a coarse map $f:X\to Y$ between metric spaces is mapped to a continuous map $\nu' f:\nu' X\to \nu' Y$ between coronas. Sheaf cohomology…
In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.
In this paper, we first discussed multiplicative metric mapping by giving some topological properties of the relevant multiplicative metric space. As an interesting result of our discussions, we observed that the set of positive real…
In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.
A uniform space is a topological space together with some additional structure which allows one to make sense of uniform properties such as completeness or uniform convergence. Motivated by previous work of J. Rivera-Letelier, we give a new…
A map between operator spaces is called completely coarse if the sequence of its amplifications is equi-coarse. We prove that all completely coarse maps must be $\mathbb R$-linear. On the opposite direction of this result, we introduce a…
Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
We propose the concepts of vicinal mappings and firmly vicinal mappings in metric spaces. We obtain fixed point and convergence theorems for these mappings in complete geodesic spaces with curvature bounded above by one and apply our…
This survey/expository article covers a variety of topics related to the "topology at infinity" of noncompact manifolds and complexes. In manifold topology and geometric group theory, the most important noncompact spaces are often…
In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms…
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…
The aim of this paper is to establish the equivalence between the concepts of an $S$-metric space and a cone $S$-metric space using\ some topological approaches. We introduce a new notion of $TVS$-cone $S$-metric space using some facts…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
For separable metrizable spaces $X,Y$ and a metrizable topological group $Z$ by $S(X\times Y,Z)$ we denote the space of all separately continuous functions $f:X\times Y\to Z$ endowed with the topology of layer-wise uniform convergence,…
On conformally compact manifolds of arbitrary signature, we use conformal geometry to identify a natural (and very general) class of canonical boundary problems. It turns out that these encompass and extend aspects of already known…
In this paper, ideas of open ball, closed ball, compact set are introduced and some related basic properties are studied. Some topological properties and some other well known results of metric spaces including Cantor intersection theorem…
This note extends the invariant defined in "An invariant of metric spaces under bornologous equivalences" to the coarse category.
We show that coarse maps between countable metric spaces of bounded geometry induce natural transformations of sufficiently good endofunctors of C*-algebras and prove that this correspondence is invariant with respect to coarse homotopies.
"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…