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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 showthat $\mathbb{R}^n/G$ has the disjoint arc-disk property.

Decompositions of $\mathbb{R}^n, n \geq 4,$ into convex sets generate codimension 1 manifold factors