The Complement of a Closed Set Satisfying the Extended Exterior Sphere Condition
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909556527857664 |
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| author | Nour, Chadi Takche, Jean |
| author_facet | Nour, Chadi Takche, Jean |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20376 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Complement of a Closed Set Satisfying the Extended Exterior Sphere Condition Nour, Chadi Takche, Jean Metric Geometry 49J52, 52A20, 93B27 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]. |
| title | The Complement of a Closed Set Satisfying the Extended Exterior Sphere Condition |
| topic | Metric Geometry 49J52, 52A20, 93B27 |
| url | https://arxiv.org/abs/2407.20376 |