• Corpus ID: 235490300

On equivalence of unbounded metric spaces at infinity

  title={On equivalence of unbounded metric spaces at infinity},
  author={Viktoriia Bilet and Oleksiy Dovgoshey},
Let (X, d) be an unbounded metric space. To investigate the asymptotic behavior of (X, d) at infinity, one can consider a sequence of rescaling metric spaces (X, 1 rn d) generated by given sequence (rn)n∈N of positive reals with rn → ∞. Metric spaces that are limit points of the sequence (X, 1 rn d)n∈N will be called pretangent spaces to (X, d) at infinity. We found the necessary and sufficient conditions under which two given unbounded subspaces of (X, d) have the same pretangent spaces at… 


Combinatorial characterization of pseudometrics
Let X, Y be sets and let $$\Phi, \Psi$$ Φ , Ψ be mappings with the domains X 2 and Y 2 respectively. We say that $$\Phi$$ Φ is combinatorially similar to $$\Psi$$ Ψ if there are bijections $$f \colon
General Topology-I
Density by moduli and Wijsman statistical convergence
In this paper, we generalized the Wijsman statistical convergence of closed sets in metric space by introducing the $f$-Wijsman statistical convergence these of sets, where $f$ is an unbounded
Local one-sided porosity and pretangent spaces
Abstract For subsets of ℝ + $\mathbb{R}^{+}$ we consider the local right upper porosity and the local right lower porosity as elements of a cluster set of all porosity numbers. The use of a scaling
Uniform boundedness of pretangent spaces
  • local constancy of metric derivatives and strong right upper porosity at a point, J. Analysis 21
  • 2013
An introduction to asymptotic geometry
This survey article presents the fundamentals of large-scale geometry of hyperbolic metric spaces and their boundaries. It is based on the book [S. Buyalo and V. Schroeder, Elements of asymptotic
Boundedness of pretangent spaces to general metric spaces
Let (X,d,p) be a metric space with a metric d and a marked point p. We define the set of w-strongly porous at 0 subsets of [0,\infty) and prove that the distance set {d(x,p): x\in X} is w-strongly
Tangent metric spaces to starlike sets on the plane
Let A ⊆ C be a starlike set with a center a. We prove that every tangent space to A at the point a is isometric to the smallest closed cone, with the vertex a, which includes A. A partial converse to
Betweenness relation and isometric imbeddings of metric spaces
We give an elementary proof of the classical Menger result according to which any metric space X that consists of more than four points is isometrically imbedded into $$ \mathbb{R} $$ if every
On real functions.