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

Abstract

We show that if $G$ is an upper semicontinuous decomposition of ${\mathbb{R}}^n$, $n\ge 4$, 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.

References in corpus (2)

• Path concordances as detectors of codimension-one manifold factors
• Detecting codimension one manifold factors with topographical techniques