Convexity in cristallographical lattices
Convexity in cristallographical lattices
复制标题
晶格中的凸性
DOI：
10.1007/bf01949705
复制
发表时间：
1973
影响因子：
0.6
通讯作者：
Jean
中科院分区：
文献类型：
--
作者：
Jean
(临界保形)格ℒn的一个子集称为凸集，只要它是格与包含ℒn的仿射空间的凸集的交集.我们给出了格的内在凸集的一个刻划，并对其他相关概念，如ℒn的凸集的边界，也给出了同样的刻划.还证明了类似于Helly定理的一个命题.
A subset of a (cristallographical) lattice ℒn is called convex whenever it is the intersection of the lattice with a convex set of the affine space containing ℒn. We give a characterization of the convex sets which is intrinsic to the lattice and do the same for other related notions, e.g. the boundary of a convex set of ℒn. A statement analogous to Helly's theorem is also proved.