Contractibility of the space of $\varepsilon$-nets in $\mathbb{R}$
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911698351292416 |
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| author | Mikhailov, Ivan N. |
| author_facet | Mikhailov, Ivan N. |
| contents | In this note, we show that the space of all $\varepsilon$-nets in the real line $\mathbb{R}$ with a natural metric, equipped with either Hausdorff or Gromov--Hausdorff distance, is contractible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19680 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contractibility of the space of $\varepsilon$-nets in $\mathbb{R}$ Mikhailov, Ivan N. Metric Geometry 51F99 In this note, we show that the space of all $\varepsilon$-nets in the real line $\mathbb{R}$ with a natural metric, equipped with either Hausdorff or Gromov--Hausdorff distance, is contractible. |
| title | Contractibility of the space of $\varepsilon$-nets in $\mathbb{R}$ |
| topic | Metric Geometry 51F99 |
| url | https://arxiv.org/abs/2605.19680 |