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arXiv · 2301.01051

The Extended Exterior Sphere Condition

Chadi Nour·Jean Takche
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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.

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Chadi Nour, Jean Takche. 2023-01-03. The Extended Exterior Sphere Condition. https://arxiv.org/abs/2301.01051

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