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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.01027 |
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| _version_ | 1866916927918571520 |
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| author | Clemens, John D. |
| author_facet | Clemens, John D. |
| contents | We show that a set of non-negative reals is the distance set of a separable complete metric space if and only if it is either countable or is an analytic set which has 0 as a limit point. We also consider spaces with simpler distance sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01027 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The set of distances in a Polish metric space Clemens, John D. Logic 03E15 We show that a set of non-negative reals is the distance set of a separable complete metric space if and only if it is either countable or is an analytic set which has 0 as a limit point. We also consider spaces with simpler distance sets. |
| title | The set of distances in a Polish metric space |
| topic | Logic 03E15 |
| url | https://arxiv.org/abs/2509.01027 |