V. Bilet

activity

20122024

most citedUniform boundedness of pretangent spaces, local constancy of metric derivatives and strong right upper porosity at a point

5 citations · 9 across the 15 of their papers we have counts for

collaborators

17 papers

math.GN2024

On monoids of metric preserving functions

Viktoriia Bilet, Oleksiy Dovgoshey

Let $X$ be a class of metric spaces and let $P_{X}$ be the set of all $f : [0, \infty) \to [0, \infty)$ preserving $X,$ $(Y, f \circ ρ) \in X$ …

math.MG2023

Pseudometric spaces. From minimality to maximality in the groups of combinatorial self-similarities

Viktoriia Bilet, Oleksiy Dovgoshey

The group of combinatorial self-similarities of a pseudometric space $(X, d)$ is the maximal subgroup of the symmetric group $Sym (X)$ whose elements preserve the four-poi…

math.GN2022

Completeness, Closedness and Metric Reflections of Pseudometric Spaces

Viktoriia Bilet, Oleksiy Dovgoshey

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…

math.CO2022

When all Permutations are Combinatorial Similarities

Viktoriia Bilet, Oleksiy Dovgoshey

Let $(X, d)$ be a semimetric space. A permutation $Φ$ of the set $X$ is a combinatorial self similarity of $(X, d)$ if there is a bijective function $f : d (X^{2}) \to d (X^{2})$ su…

math.MG2021

On equivalence of unbounded metric spaces at infinity

Viktoriia Bilet, 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, \frac{1}{r_n}…

math.MG2021

Ultrametrics and complete multipartite graphs

Viktoriia Bilet, Oleksiy Dovgoshey, Yuriy Kononov

We describe the class of graphs for which all metric spaces with diametrical graphs belonging to this class are ultrametric. It is shown that a metric space $(X, d)$ is ultrametric…

math.GN2020

Ultrametric preserving functions and weak similarities of ultrametric spaces

Viktoriia Bilet, Oleksiy Dovgoshey, Ruslan Shanin

Let $W S (X, d)$ be the class of ultrametric spaces which are weakly similar to ultrametric space $(X, d)$ . The main results of the paper completely describe the ultrametric spaces $…

math.MG2018★ 1 cited

Finite asymptotic clusters of metric spaces

Viktoriia Bilet, Oleksiy Dovgoshey

Let $(X, d)$ be an unbounded metric space and let $r ~ = (r_{n})_{n \in N}$ be a sequence of positive real numbers tending to infinity. A pretangent space $Ω_{\infty, \tilde…

math.MG2017★ 1 cited

Asymptotic structure of general metric spaces at infinity

Viktoriia Bilet, Oleksiy Dovgoshey

Let $(X, d)$ be an unbounded metric space and $r ~ = (r_{n})_{n \in N}$ be a scaling sequence of positive real numbers tending to infinity. We define the pretangent space $Ω_…

math.MG2017

Asymptotic behavior of metric spaces at infinity

Viktoriia Bilet, Oleksiy Dovgoshey

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.

math.CA2016★ 1 cited

Boundedness of Lebesgue constants and interpolating Faber bases

Viktoriia Bilet, Oleksiy Dovgoshey, Jürgen Prestin

We investigate some conditions under which the Lebesgue constants or Lebesgue functions are bounded for the classical Lagrange polynomial interpolation on a compact subset of $\mat…

math.MG2014★ 5 cited

Uniform boundedness of pretangent spaces, local constancy of metric derivatives and strong right upper porosity at a point

Viktoriia Bilet, Oleksiy Dovgoshey, Mehmet Kucukaslan

Let $(X, d, p)$ be a pointed metric space. A pretangent space to $X$ at $p$ is a metric space consisting of some equivalence classes of convergent to $p$ sequences $(x_n), x_n \in X,…

math.CA2014

Two ideals connected with strong right upper porosity at a point

V. Bilet, O. Dovgoshey, J. Prestin

Let $S P$ be the set of upper strongly porous at $0$ subsets of $R^{+}$ and let $I^(S P)$ be the intersection of maximal ideals $I \subseteq S P$ . Some characteristic prop…

math.MG2013

Uniform boundedness of pretangent spaces and local strong one-side porosity

Viktoriia Bilet, Oleksiy Dovgoshey

Let (X,d,p) be a pointed metric space. A pretangent space to X at p is a metric space consisting of some equivalence classes of convergent to p sequences (x_n), x_n \in X, whose de…

math.MG2013★ 1 cited

Pretangent spaces with nonpositive and nonnegative Aleksandrov curvature

Viktoriia Bilet, Oleksiy Dovgoshey

We find conditions under which the pretangent spaces to general metric spaces have the nonpositive Aleksandrov curvature or nonnegative one. The infinitesimal structure of general…

math.MG2012

Boundedness of pretangent spaces to general metric spaces

Viktoriia Bilet, Oleksiy Dovgoshey

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…

math.CA2012

A kind of local strong one-side porosity

O. Dovgoshey, V. Bilet

We define and study the completely strongly porous at 0 subsets of R^{+}. Several characterizations of these subsets are obtained, among them the description via an universal prope…