摘要
在巴拿赫空间理论中,Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一,分隔性定理是Hahn-Banach定理的重要应用,本文利用"超平面"的方法,改进了一个分隔性定理的证明;另外,本文利用邻域的"平移"方法,给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。
<Abstrcat>In the theory of Banach Space,Hahn-Banach extension theorem is well known as one of three basic theorems of Banach Space and the separation theorem is one important applieation.In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.
出处
《河北建筑科技学院学报》
2005年第2期111-112,共2页
Journal of Hebei Institute of Architectural Science & Technology
关键词
赋范线性空间
线性泛函
次凸泛函
超平面
邻域平移
normed linear space
linear function
subconvex function
hyperplane
moving neighborhood
