On a subclass of the family of Darboux functions
Tom 117 / 2009
Colloquium Mathematicum 117 (2009), 95-104 MSC: Primary 26A15. DOI: 10.4064/cm117-1-6
We investigate functions $f:I\to \mathbb R$ (where $I$ is an open interval) such that for all $u,v\in I$ with $u < v$ and $f(u)\neq f(v)$ and each $c\in (\min(f(u),f(v)),\max(f(u),f(v)))$ there is a point $w\in (u,v)$ such that $f(w) = c$ and $f$ is approximately continuous at $w$.