Gromov-Hausdorff distances between normed spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913411836674048 |
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| author | Mikhailov, I. N. |
| author_facet | Mikhailov, I. N. |
| contents | In the present paper we study the original Gromov-Hausdorff distance between real normed spaces. In the first part of the paper we prove that two finite-dimensional real normed spaces on a finite Gromov-Hausdorff distance are isometric to each other. We then study the properties of finite point sets in finite-dimensional normed spaces whose cardinalities exceed the equilateral dimension of an ambient space. By means of the obtained results we prove the following enhancement of the aforementioned theorem: every finite-dimensional normed space lies on an infinite Gromov-Hausdorff distance from all other non-isometric normed spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gromov-Hausdorff distances between normed spaces Mikhailov, I. N. Metric Geometry In the present paper we study the original Gromov-Hausdorff distance between real normed spaces. In the first part of the paper we prove that two finite-dimensional real normed spaces on a finite Gromov-Hausdorff distance are isometric to each other. We then study the properties of finite point sets in finite-dimensional normed spaces whose cardinalities exceed the equilateral dimension of an ambient space. By means of the obtained results we prove the following enhancement of the aforementioned theorem: every finite-dimensional normed space lies on an infinite Gromov-Hausdorff distance from all other non-isometric normed spaces. |
| title | Gromov-Hausdorff distances between normed spaces |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2407.01388 |