Continuous colorings on compact spaces

Fuente: arXiv
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Main Authors: de Rancourt, Noé, Lecomte, Dominique, Zelen, Miroslav
Format: Preprint
Published: 2025
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_version_ 1866916963958128640
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