English

A nonsmooth path-connectedness relation in the real plane

Logic 2025-02-18 v2

Abstract

In this paper, we construct a compact subset of the real plane whose path-connectedness equivalence relation is Borel bireducible to a nonsmooth hyperfinite Borel equivalence relation. This answers a question of \cite{bec98}.

Cite

@article{arxiv.2501.07916,
  title  = {A nonsmooth path-connectedness relation in the real plane},
  author = {Yusuf Uyar},
  journal= {arXiv preprint arXiv:2501.07916},
  year   = {2025}
}
R2 v1 2026-06-28T21:05:36.838Z