Continuous colorings on compact spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916963958128640 |
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| author | de Rancourt, Noé Lecomte, Dominique Zelen, Miroslav |
| author_facet | de Rancourt, Noé Lecomte, Dominique Zelen, Miroslav |
| contents | We study several natural classes of graphs on a zero-dimensional metrizable compact space having no continuous coloring. We compare these graphs with the quasi-order associated with injective continuous homomorphisms. We prove the existence of an antichain basis for these classes. We determine the size of such an antichain basis. We provide a concrete antichain basis when there is a countable one. We also provide some related quasi-orders and equivalence relations which are analytic complete as sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous colorings on compact spaces de Rancourt, Noé Lecomte, Dominique Zelen, Miroslav General Topology Logic We study several natural classes of graphs on a zero-dimensional metrizable compact space having no continuous coloring. We compare these graphs with the quasi-order associated with injective continuous homomorphisms. We prove the existence of an antichain basis for these classes. We determine the size of such an antichain basis. We provide a concrete antichain basis when there is a countable one. We also provide some related quasi-orders and equivalence relations which are analytic complete as sets. |
| title | Continuous colorings on compact spaces |
| topic | General Topology Logic |
| url | https://arxiv.org/abs/2509.18680 |