关于凸曲面的几个定义的关系

Relations of Definitions of Convex surface

本文讨论了凸曲面的几种定义及其关系,发现有的定义是局部凸的定义,有的是整体凸的定义,有的则对于局部凸和整体凸都适合,最后给出了各种定义之间互推的证明,对于局部凸和整体凸定义之间不能推证的,则说明了原因.

In the paper,the kinds of define of convex surface and their relations some definition fits defining local convex, some definition fits global convexity, local convexity and global convex ity are found. At last ,commutative deducibility and reason is explained if cannot infer another definition from one definition. are discussed,the facts that some definition fits both of of some definitions is given,