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arXiv · 2509.18680

Continuous colorings on compact spaces

Noé de Rancourt·Dominique Lecomte·Miroslav Zelen
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Abstract

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.

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Noé de Rancourt, Dominique Lecomte, Miroslav Zelen. 2025-09-23. Continuous colorings on compact spaces. https://arxiv.org/abs/2509.18680

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