• 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… 
1 Citations
Completeness, Closedness and Metric Reflections of Pseudometric Spaces
. It is well-known that a metric space ( X, d ) is complete iff the set X is closed in every metric superspace of ( X, d ) . For a given pseudometric space ( Y, ρ ) , we describe the maximal class CEC


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 $$f \colon
An introduction to asymptotic geometry
This survey article presents the fundamentals of large-scale geometry of hyperbolic metric spaces and their boundaries. It is based on the book [S. Buyalo and V. Schroeder, Elements of asymptotic
Betweenness relation and isometric imbeddings of metric spaces
We give an elementary proof of the classical Menger result according to which any metric space X that consists of more than four points is isometrically imbedded into $$ \mathbb{R} $$ if every
Elements of Asymptotic Geometry
Asymptotic geometry is the study of metric spaces from a large scale point of view, where the local geometry does not come into play. An important class of model spaces are the hyperbolic spaces (in
Topologies on Closed and Closed Convex Sets
Preface. 1. Preliminaries. 2. Weak Topologies determined by Distance Functionals. 3. The Attouch--Wets and Hausdorff Metric Topologies. 4. Gap and Excess Functionals and Weak Topologies. 5. The Fell
Wijsman convergence in the hyperspace of a metric space
An improved interface circuit for use between variable voltage analog sensors which are measuring physical parameters and a microprocessor which is processing the data relating to such parameters.
On real functions.
Lectures on coarse geometry
Metric spaces Coarse spaces Growth and amenability Translation algebras Coarse algebraic topology Coarse negative curvature Limits of metric spaces Rigidity Asymptotic dimension Groupoids and coarse