Monovex sets
Volume 242 / 2018
Studia Mathematica 242 (2018), 165-178
MSC: Primary 52A30; Secondary 47H10.
DOI: 10.4064/sm8765-7-2017
Published online: 5 February 2018
Abstract
A set $A$ in a finite-dimensional Euclidean space is monovex if for any $x,y \in A$ 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.
