The relative Chebyshev center of a finite set in a geodesic space

In the present paper we estimate variation in the relative Chebyshev radius $R_W(M)$, where $M$ and $W$are nonempty bounded sets of a metric space, as the sets $M$ and $W$ change. We find the closure and the interior of the set of all $N$-nets each of which contains its unique relative Chebyshev center, in the set of all $N$-nets of a special geodesic space endowed by the Hausdorff metric. We consider various properties of relative Chebyshev centers of a finite set which lie in this set.