球面分离定理
Spherical Separation Theorem
摘要：
在本文中，它表明，对于任何两个非空闭（分别为，open）和$S^n$的球面凸子集$\mathcal{W}_1, \mathcal{W}_2$，交集$\mathcal{W}_1\cap \mathcal{W}_2$为空当且仅当子集$\{P\in S^n\; |\; P\cdot Q>0 \mbox{ for any } Q\in \mathcal{W}_1 \mbox{ and } P\cdot R<0 \mbox{ for any } R\in \mathcal{W}_2\}$为非空，open（分别，闭）和球形凸。
英文摘要：
In this paper, it is shown that for any two non-empty closed (resp., open) and spherical convex subsets $\mathcal{W}_1, \mathcal{W}_2$ of $S^n$, the intersection $\mathcal{W}_1\cap \mathcal{W}_2$ is empty if and only if the subset $\{P\in S^n\; |\; P\cdot Q>0 \mbox{ for any } Q\in \mathcal{W}_1 \mbox{ and } P\cdot R<0 \mbox{ for any } R\in \mathcal{W}_2\}$ is non-empty, open (resp., closed) and spherical convex.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
