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arXiv · 2412.18949

Metric Space Recognition by Gromov-Hausdorff Distances to Simplexes

A. O. Ivanov·E. S. Lychagina·A. A. Tuzhilin
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Abstract

In the present paper a distinguishability of bounded metric spaces by the set of the Gromov--Hausdorff distances to so-called simplexes (metric spaces with unique non-zero distance) is investigated. It is easy to construct an example of non-isometric metric spaces such that the Gromov--Hausdorff distance between them vanishes. Such spaces are non-distinguishable, of course. But we give examples of non-distinguishable metric spaces, the Gromov--Hausdorff distance between which is non-zero. More over, we prove several sufficient and necessary conditions for metric spaces to be non-distinguishable.

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A. O. Ivanov, E. S. Lychagina, A. A. Tuzhilin. 2024-12-25. Metric Space Recognition by Gromov-Hausdorff Distances to Simplexes. https://arxiv.org/abs/2412.18949

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