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

Denise M. Halverson; Dušan Repovš

doi:10.1007/s00009-012-0197-1

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arXiv · 1304.6956

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

Denise M. Halverson·Dušan Repovš

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Abstract

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.

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Denise M. Halverson, Dušan Repovš. 2013-05-04. Decompositions of $\mathbb{R}^n, n \geq 4,$ into convex sets generate codimension 1 manifold factors. https://doi.org/10.1007/s00009-012-0197-1

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