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| 摘要: |
| 本文研究了欧式空间单位球面Sn-1上秋凸集的定义与基本性质.利用径向函数，定义了空间中有限个点的凸组合运算，并由此给出了Sn-1上球凸集的分析定义和集合球凸包的定义.讨论了球凸集和球凸包的基础性质.最后证明了任一闭球凸集都可以表示为其端点集的球凸包.这个结论的形成与获证完全得益于本文采用的分析方法. |
| 关键词: 球面凸集 球面凸组合 径向函数 凸包 锥包 |
| DOI： |
| 分类号:O184;O177.99 |
| 基金项目:Supported by the National Natural Science Foundation of China (11671293; 11271282). |
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| ANALYTIC APPROACH TO SPHERICALLY CONVEX SETS IN Sn-1 |
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SHAO Yu-cheng,GUO Q
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| Abstract: |
| This article concerns with the definition and elementary properties of spherically convex sets in the Euclidean unit sphere Sn-1. First, we define the spherically convex combination of finitely many elements in the Euclidean spaces, in terms of which the spherically convex set and the spherically convex hull of sets in Sn-1 are defined, then study the properties of the spherically convex sets and hulls. Finally, we prove that each closed spherically convex set can be expressed as the spherically convex hull of its extreme point set, the formulation and proof of which benifit from the analytic approach adopted in this paper. |
| Key words: spherically convex set spherically convex combination radial function convex hull conical hull |
