The Extended Exterior Sphere Condition
Metric Geometry
2024-02-27 v1
Abstract
We prove that the complement of a closed set S satisfying an extended exterior sphere condition is nothing but the union of closed balls with common radius. This generalizes [11, Theorem 3] where the set S is assumed to be prox-regular, a property stronger than the extended exterior sphere condition. We also provide a sufficient condition for the equivalence between prox-regularity and the extended exterior sphere condition that generalizes [13, Corollary 3.12] to the case in which S is not necessarily regular closed.
Cite
@article{arxiv.2301.01051,
title = {The Extended Exterior Sphere Condition},
author = {Chadi Nour and Jean Takche},
journal= {arXiv preprint arXiv:2301.01051},
year = {2024}
}