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The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces (1907.03828v1)
Published 8 Jul 2019 in math.MG
Abstract: In the present paper we investigate the Gromov--Hausdorff distances between a bounded metric space $X$ and so called simplex, i.e., a metric space all whose non-zero distances are the same. In the case when the simplex's cardinality does not exceed the cardinality of $X$, a new formula for this distance is obtained. The latter permits to derive an exact formula for the distance between a simplex and an ultrametric space.