满足扩展外球面条件的封闭集的补集

arXiv - MATH - Metric Geometry Pub Date : 2024-07-29 DOI:arxiv-2407.20376

Chadi Nour, Jean Takche

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引用次数: 0

摘要

我们为[10，定理 3.1]的改进版提供了一个新颖的分析证明，表明满足扩展外球面条件的闭集的补集只不过是具有较低连续半径函数的闭球的联合。改进之处在于半径函数，现在它比 [10, 定理 3.1] 中使用的函数更大。

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The Complement of a Closed Set Satisfying the Extended Exterior Sphere Condition

We provide a novel analytical proof of an improved version of [10, Theorem 3.1], showing that the complement of a closed set satisfying the extended exterior sphere condition is nothing but the union of closed balls with lower semicontinuous radius function. The improvement lies in the radius function, which is now larger than the one used in [10, Theorem 3.1].

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arXiv - MATH - Metric Geometry

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