Monovex Sets
Lev Buhovsky, Eilon Solan, Omri Nisan Solan

TL;DR
This paper investigates monovex sets in Euclidean spaces, proving that open and closed monovex sets are contractible and providing a counterexample for nonopen, nonclosed sets, thus revealing key topological properties.
Contribution
The paper establishes contractibility of open and closed monovex sets and presents a counterexample for nonopen, nonclosed monovex sets, advancing understanding of their topological structure.
Findings
Open and closed monovex sets are contractible.
Counterexample of a nonopen, nonclosed monovex set that is not contractible.
Additional properties of monovex sets are revealed.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsOptimization and Variational Analysis
