3 papers
math.LO2026
The Complexity of Arc-Connectedness Relation in the Plane
Yusuf Uyar
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…
math.GN2026
The Complexity of Connectedness Relations on Polish Spaces
Michal Hevessy, Yusuf Uyar, Benjamin Vejnar
We systematically investigate three different equivalence relations of connectedness: being connected by arcs, being connected by continua and being connected by chains of continua…
math.LO2025
A nonsmooth path-connectedness relation in the real plane
Yusuf Uyar
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 relat…