Calculating Gromov-Hausdorff distance by means of asymptotic dimension
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913857348304896 |
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| author | Mikhailov, Ivan N. |
| author_facet | Mikhailov, Ivan N. |
| contents | In this paper, we apply the concept of asymptotic dimension to calculating Gromov-Hausdorff distances between some unbounded metric spaces. For example, we show that the Gromov--Hausdorff between $\mathbb{R}^2$ with the Euclidean metric and $\mathbb{Z}^2$ equals the Hausdorff distance between them: $d_{GH}(\mathbb{R}^2, \mathbb{Z}^2) = d_H(\mathbb{R}^2, \mathbb{Z}^2)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_18158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Calculating Gromov-Hausdorff distance by means of asymptotic dimension Mikhailov, Ivan N. Metric Geometry 51F99 In this paper, we apply the concept of asymptotic dimension to calculating Gromov-Hausdorff distances between some unbounded metric spaces. For example, we show that the Gromov--Hausdorff between $\mathbb{R}^2$ with the Euclidean metric and $\mathbb{Z}^2$ equals the Hausdorff distance between them: $d_{GH}(\mathbb{R}^2, \mathbb{Z}^2) = d_H(\mathbb{R}^2, \mathbb{Z}^2)$. |
| title | Calculating Gromov-Hausdorff distance by means of asymptotic dimension |
| topic | Metric Geometry 51F99 |
| url | https://arxiv.org/abs/2505.18158 |