24 citations · 98 across the 69 of their papers we have counts for
6 papers · 1 filter
Bipartite graphs and best proximity pairs
Karim Chaira, Oleksiy Dovgoshey, Samih Lazaiz
We say that a bipartite graph with fixed parts , is proximinal if there is a semimetric space such that and are disjoint proximinal subsets of …
Best proximity pairs in ultrametric spaces
K. Chaira, O. Dovgoshey, S. Lazaiz
In the present paper, we study the existence of best proximity pairs in ultrametric spaces. We show, under suitable assumptions, that the proximinal pair has a best proximi…
On equivalence of unbounded metric spaces at infinity
Viktoriia Bilet, Oleksiy Dovgoshey
Let be an unbounded metric space. To investigate the asymptotic behavior of at infinity, one can consider a sequence of rescaling metric spaces $(X, \frac{1}{r_n}…
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 is ultrametric…
The range of ultrametrics, compactness, and separability
Oleksiy Dovgoshey, Volodymir Shcherbak
We describe the order type of range sets of compact ultrametrics and show that an ultrametrizable infinite topological space is compact iff the range sets are order isomor…
Labeled trees generating complete, compact, and discrete ultrametric spaces
Oleksiy Dovgoshey, Mehmet Küçükaslan
We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ul…