The Variable Radius Form of the Extended Exterior Sphere Condition
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915108512333824 |
|---|---|
| author | Nour, Chadi Takche, Jean |
| author_facet | Nour, Chadi Takche, Jean |
| contents | We introduce a variable radius form of the extended exterior sphere condition of [16], and then, we prove that the complement of a closed set satisfying this new property is nothing but the union of closed balls with lower semicontinous radius function. This generalizes, to the variable radius case, the main result of [16], namely, [16, Theorem 1.2]. On the other hand, as it is shown in [14,15] for prox-regularity, the exterior sphere condition, and the union of closed balls property, we prove that the constant and the variable radius forms of the extended exterior sphere condition belong to the S-convexity regularity class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04707 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Variable Radius Form of the Extended Exterior Sphere Condition Nour, Chadi Takche, Jean Metric Geometry 49J52, 52A20, 93B27 We introduce a variable radius form of the extended exterior sphere condition of [16], and then, we prove that the complement of a closed set satisfying this new property is nothing but the union of closed balls with lower semicontinous radius function. This generalizes, to the variable radius case, the main result of [16], namely, [16, Theorem 1.2]. On the other hand, as it is shown in [14,15] for prox-regularity, the exterior sphere condition, and the union of closed balls property, we prove that the constant and the variable radius forms of the extended exterior sphere condition belong to the S-convexity regularity class. |
| title | The Variable Radius Form of the Extended Exterior Sphere Condition |
| topic | Metric Geometry 49J52, 52A20, 93B27 |
| url | https://arxiv.org/abs/2403.04707 |