Monovex Sets
General Topology
2016-09-29 v1
Abstract
A set in a finite dimensional Euclidean space is \emph{monovex} if for every two points there is a continuous path within the set that connects and 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.
Cite
@article{arxiv.1609.08844,
title = {Monovex Sets},
author = {Lev Buhovsky and Eilon Solan and Omri Nisan Solan},
journal= {arXiv preprint arXiv:1609.08844},
year = {2016}
}