Helly定理的几何特征

THE GEOMETRICAL CHARACTER OF HELLY'S THEOREM

线性赋范空间理论中的Ｈｅｌｌｙ定理的证明一般都是借助于深刻的开映射定理和线性泛函的Ｈａｈｎ—Ｂａｎａｃｈ扩张定理（几何形式），而且，任意＞０的意义是不明确的．文中给出Ｈｅｌｌｙ定理一个简单、初等的证明（仅用到商空间的概念）．它具有显明的几何特征而且澄清了任意＞０的几何意义．

in general, the proof of the Helly's theorem in the theory of normed linear spaces is based on the deeper' open mapping theorem' and the 'Hahn-Banach's extension theorem (in geometrical version', and the meaning of the arbitary 0 is indistinct. This artical gives the Helly' theorem a simple-and primary proof (use only the notion of guotient spaces),which has clean geometrical character and clearifies the geometrieal meaning of arbitary .