The descriptive complexity of the set of arc-connected compact subsets of the plane
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914263766925312 |
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| author | Debs, Gabriel Raymond, Jean Saint |
| author_facet | Debs, Gabriel Raymond, Jean Saint |
| contents | We compute the exact complexity of the set of all arc-connected compact subsets of $\boldmath R^2$, which turns out to be strictly higher than the classical $\boldmath Σ^1_1$ and $\boldmath Π^1_1$ classes of analytic and coanalytic sets, but stricly lower than the class $\boldmath Π^1_2$ which is the exact descriptive class of the set of all arc-connected compact subsets of $\boldmath R^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13135 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The descriptive complexity of the set of arc-connected compact subsets of the plane Debs, Gabriel Raymond, Jean Saint General Topology Logic 54H05, 03E15 We compute the exact complexity of the set of all arc-connected compact subsets of $\boldmath R^2$, which turns out to be strictly higher than the classical $\boldmath Σ^1_1$ and $\boldmath Π^1_1$ classes of analytic and coanalytic sets, but stricly lower than the class $\boldmath Π^1_2$ which is the exact descriptive class of the set of all arc-connected compact subsets of $\boldmath R^3$. |
| title | The descriptive complexity of the set of arc-connected compact subsets of the plane |
| topic | General Topology Logic 54H05, 03E15 |
| url | https://arxiv.org/abs/2601.13135 |