Continuous colorings on compact spaces
General Topology
2025-09-24 v1 Logic
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.
Cite
@article{arxiv.2509.18680,
title = {Continuous colorings on compact spaces},
author = {Noé de Rancourt and Dominique Lecomte and Miroslav Zelen},
journal= {arXiv preprint arXiv:2509.18680},
year = {2025}
}