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.
- Contractible sets
- Monovex sets