E^n中的开集不存在最小凸生成集

On the Existence of Minimal Convex Generated Set in the Open Set of E^n

对于紧凸集 ,文献 [1 ]中有定理 :S为En 中的紧凸集 ,则S是其轮廓的凸包 ,即对于En 中的紧凸集 ,其轮廓就是其最小凸生成集 本文证明了En

For compact convex sets,there is a theorem in the book^([1]):“Let S be a compact convex subset of E^n,then S is the convex hull of its profile.” That is, for a compact convex set of E^n,its profile is its minimal convex generated set.In this paper,we prove that there is no minimal convex generated set in the open set of E^n.