R. Shanin

activity

20202025

collaborators

3 papers

math.GN2025

On the closure of one point sets in $T_0$-spaces

Oleksiy Dovgoshey, Ruslan Shanin

Let $X$ be a set and $2^{X}$ be a set of all subsets of $X$ . The necessary and sufficient conditions under which a mapping $X \to 2^{X}$ is a closure of one-point sets in some $T_{0}$ -sp…

math.GN2022

Uniqueness of best proximity pairs and rigidity of semimetric spaces

Oleksiy Dovgoshey, Ruslan Shanin

For arbitrary semimetric space $(X, d)$ and disjoint proximinal subsets $A$ , $B$ of $X$ we define the proximinal graph as a bipartite graph with parts $A$ and $B$ whose edges $\{a,…

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 $…

On the closure of one point sets in \(T_0\)-spaces

Uniqueness of best proximity pairs and rigidity of semimetric spaces

Ultrametric preserving functions and weak similarities of ultrametric spaces