Work

Failure of the $G_0$-dichotomy for generalized Cantor spaces

Year: 2026

Type: preprint

Abstract: Kechris, Solecki and Todorčević's $G_0$-dichotomy characterizes Borel graphs that admit a Borel measurable coloring with countably many colors. We show that the analogue to the $G_0$-dichotomy for generalized Cantor spaces fails at the lowest possible complexity, namely for closed graphs.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.07450

Authors: Casarosa, Matteo, Schlicht, Philipp

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Università Italo Francese, Universitat de Barcelona

OpenAlex ID: W7212080020

Cites: 2

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Related to: 10