关于Krein-Milman定理的一点注记

A note on the Krein-Milman theorem

目的研究线性拓扑空间中紧集端点存在性问题。方法集合论与点集拓扑学中的方法。结果得到一般线性拓扑空间中紧集端点存在的一个充分必要条件。结论证明局部凸线性拓扑空间中的紧集必有端点,同时给出Krein-M ilman定理的简化证明。

Aim To study the existence of the extreme points of a compact set in linear topological space. Methods Using method of the theory of set and general topology. Results A sufficient and necessary condition of the exist- ence of the extreme points of a compact set in linear topological space was obtained. Conclusion The theorem proved that the extreme points of a compact set in locally convex linear topological space must exist. Then the Krein-Milman theorem was reproved with a very simple method.