The Complexity of Arc-Connectedness Relation in the Plane
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917185383825408 |
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| author | Uyar, Yusuf |
| author_facet | Uyar, Yusuf |
| contents | In this paper, we show that the arc-connectedness equivalence relation on a Polish subspace of the real plane is an essentially hyperfinite Borel equivalence relation. This result provides the optimal upper bound for such a Borel equivalence relation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Complexity of Arc-Connectedness Relation in the Plane Uyar, Yusuf Logic In this paper, we show that the arc-connectedness equivalence relation on a Polish subspace of the real plane is an essentially hyperfinite Borel equivalence relation. This result provides the optimal upper bound for such a Borel equivalence relation. |
| title | The Complexity of Arc-Connectedness Relation in the Plane |
| topic | Logic |
| url | https://arxiv.org/abs/2509.24596 |