Monovex Sets

Lev Buhovsky; Eilon Solan; Omri Nisan Solan

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arXiv · 1609.08844

Monovex Sets

Lev Buhovsky·Eilon Solan·Omri Nisan Solan

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Abstract

A set $A$ in a finite dimensional Euclidean space is \emph{monovex} if for every two points $x,y \in A$ there is a continuous path within the set that connects $x$ and $y$ and is monotone (nonincreasing or nondecreasing) in each coordinate. We prove that every open monovex set as well as every closed monovex set is contractible, and provide an example of a nonopen and nonclosed monovex set that is not contractible. Our proofs reveal additional properties of monovex sets.

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BibTeX RIS

Lev Buhovsky, Eilon Solan, Omri Nisan Solan. 2016-09-28. Monovex Sets. https://arxiv.org/abs/1609.08844

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