Geometry of compact metric space in terms of Gromov-Hausdorff distances to regular simplexes
AO Ivanov, AA Tuzhilin - arXiv preprint arXiv:1607.06655, 2016 - arxiv.org
In the present paper we investigate geometric characteristics of compact metric spaces,
which can be described in terms of Gromov-Hausdorff distances to simplexes, ie, to finite
metric spaces such that all their nonzero distances are equal to each other. It turns out that
these Gromov-Hausdorff distances depend on some geometrical characteristics of finite
partitions of the compact metric spaces; some of the characteristics can be considered as a
natural analogue of the lengths of edges of minimum spanning trees. As a consequence, we …
which can be described in terms of Gromov-Hausdorff distances to simplexes, ie, to finite
metric spaces such that all their nonzero distances are equal to each other. It turns out that
these Gromov-Hausdorff distances depend on some geometrical characteristics of finite
partitions of the compact metric spaces; some of the characteristics can be considered as a
natural analogue of the lengths of edges of minimum spanning trees. As a consequence, we …
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