2016/09/28 by Lev Buhovsky, Buhovsky, Lev, Eilon Solan +3
Computer Science · #47H10 #52A30 #52A37 #FOS: Mathematics #General Topology (math.GN) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1609.08844
openalex publication_date 2016/09/28 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
A set A in a finite dimensional Euclidean space is monovex if for every two points x,y ∈ 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.