On Hausdorff intrinsic metric

Abstract

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