Center of distances of ultrametric spaces generated by labeled trees
Oleksiy Dovgoshey, Olga Rovenska

TL;DR
This paper investigates the properties of the center of distances in ultrametric spaces generated by labeled trees, providing conditions for when the center includes the diameter of the space.
Contribution
It characterizes the center of distances in ultrametric spaces from labeled trees and establishes necessary and sufficient conditions for including the diameter.
Findings
C(X) is either {0} or {0, diam X} for these spaces.
Conditions for diam X to be in C(X) are identified.
Provides a complete description of the center of distances in this context.
Abstract
The center of distances of a metric space is the set of all for which the equation has a solution for each . We prove that the equalities or hold if is an ultrametric space generated by labeled trees. The necessary and sufficient conditions under which are found.
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Taxonomy
TopicsFixed Point Theorems Analysis · advanced mathematical theories · Functional Equations Stability Results
