3 papers
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
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.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…