Monovex sets

Lev Buhovsky; Eilon Solan; Omri N. Solan

doi:10.4064/sm8765-7-2017

Monovex sets

Lev Buhovsky, Eilon Solan, Omri N. Solan

Research output: Contribution to journal › Article › peer-review

Abstract

A set A in a finite-dimensional Euclidean space is monovex if for any x; y ϵ A there is a continuous path within A that connects x and y and is monotone (nonincreasing or nondecreasing) in each coordinate. We prove that every open monovex set and every closed monovex set are contractible, and we provide an example of a nonopen and nonclosed monovex set that is not contractible. Our proofs reveal additional properties of monovex sets.

Original language	English
Pages (from-to)	165-178
Number of pages	14
Journal	Studia Mathematica
Volume	242
Issue number	2
DOIs	https://doi.org/10.4064/sm8765-7-2017
State	Published - 2018

Keywords

Contractible sets
Monovex sets

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10.4064/sm8765-7-2017

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Monovex sets

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Keywords

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