On Hausdorff intrinsic metric
(Lobachevskii Journal of Mathematics, Volume VIII)
In this paper we prove that in the set of all nonempty bounded closed subsets of a metric space (X,ρ ) the Hausdorff metric is the Hausdorff intrinsic metric if and only if the metric ρ is an intrinsic metric. In a space with an intrinsic metric we obtain the upper bound for the Hausdorff distance between generalized balls.