E. N. Sosov

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.
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