  We show that if $G$ is an upper semicontinuous decomposition of
$\mathbb{R}^n$, $n \geq 4$, into convex sets, then the quotient space
$\mathbb{R}^n/G$ is a codimension one manifold factor. In particular, we show
that $\mathbb{R}^n/G$ has the disjoint arc-disk property.
