Year: 2020
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Han, Huhe, Nishimura, Takashi
Institutions: Northwest A&F University, Yokohama National University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3006146664