Year: 2026
Type: preprint
Abstract: We prove that topological conjugacy and flip conjugacy of minimal homeomorphisms of a Cantor space are complete analytic relations and hence are not Borel. We also prove that mutual reducibility by injective continuous graph homomorphisms and topological graph isomorphism are complete analytic relations on the space of nonempty compact graphs on a fixed Cantor vertex space with continuous chromatic number two. Both relations remain complete analytic on the larger space of nonempty compact graphs on the same Cantor vertex space with continuous chromatic number two or three.
Source: arXiv (Cornell University)
Institution: Jagiellonian University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213234943