The Complexity of Arc-Connectedness Relation in the Plane
Logic
2026-01-07 v2
Abstract
In this paper, we show that the arc-connectedness equivalence relation on a Polish subspace of the real plane is an essentially hyperfinite Borel equivalence relation. This result provides the optimal upper bound for such a Borel equivalence relation.
Cite
@article{arxiv.2509.24596,
title = {The Complexity of Arc-Connectedness Relation in the Plane},
author = {Yusuf Uyar},
journal= {arXiv preprint arXiv:2509.24596},
year = {2026}
}