Ω-凸集的组合与结构性质（英文）

The Combinatorial and Structural Properties of Ω-Convex Sets

本文研究Ω-凸集的组合性质和结构性质.在一定条件下,证明关于Ω-凸集的Randon型定理,Helly型定理.Caratheodory型定理以及Minkowski型定理,并举例说明对一般的Ω-凸集这些定理不一定成立.文中所得结果是关于凸集的这些类型定理的推广,同时也为有关Ω-凸函数的研究提供了理论工具.

In this paper, we discuss the combinatorial and structural properties ofΩ-convex sets. Theorems of Radon’s, Helly’s, Caratheodory’s and Minkowski’s type for Ω-convex sets are proved under some conditions even if they are not valid for Ω-convex sets in general. These results are extensions and variations of the classical fundamental theorems of such types for convex sets,which at the same time provide some useful tools in the study on Ω-functions.