Metric Space Recognition by Gromov-Hausdorff Distances to Simplexes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913627239350272 |
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| author | Ivanov, A. O. Lychagina, E. S. Tuzhilin, A. A. |
| author_facet | Ivanov, A. O. Lychagina, E. S. Tuzhilin, A. A. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_18949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metric Space Recognition by Gromov-Hausdorff Distances to Simplexes Ivanov, A. O. Lychagina, E. S. Tuzhilin, A. A. Metric Geometry 51F99 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. |
| title | Metric Space Recognition by Gromov-Hausdorff Distances to Simplexes |
| topic | Metric Geometry 51F99 |
| url | https://arxiv.org/abs/2412.18949 |