论文标题
球形分离定理
Spherical Separation Theorem
论文作者
论文摘要
在本文中，可以表明，对于任何两个非空封闭（分别，打开）和球形凸子集$ \ MATHCAL {W} _1，\ MATHCAL {W} _2 $ of $ s^n $，交叉点$ \ MATHCAL {W} $ \ {p \ in S^n \; | \; p \ cdot q> 0 \ mbox {对于任何} q \ in \ nathcal {w} _1 \ mbox {and} p \ cdot r <0 \ 0 \ mbox {对于任何} r \ in \ intcal {w} _2 \} _2 \} $ nockient，npecky opent opent opent opent opent opent opent opent opent（prock）。
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.
