非Dedekind完备的序拓扑向量空间中集值映射的一类扩张  

Extensions of Set-valued Mapping on Non-Dedeking complete Ordered Topological Vector Spaces

作　　者：肖斌贝 刘信东[1] 

机构地区：[1]宜宾学院数学系,四川宜宾644007

出　　处：《成都信息工程学院学报》2010年第3期336-340,共5页Journal of Chengdu University of Information Technology

摘　　要：在泛函分析中有着重要作用的Hahn-Banach扩张定理及其很多推广定理的条件都要求值域空间是Dedekind完备的,这是一个非常强的条件,因而在一定程度上局限了这些扩张定理的应用。主要考虑弱化这些定理的条件,讨论当值域空间是由锥引入序的非Dedekind完备的序拓扑向量空间时,一类集值映射的扩张。In functional analysis, the classical Hahn-Banach extension theorem and most of its generalization play a very important role on condition that the value space must be a Dedekind complete vector space. In this paper, we also show that a extension theorem concerning set-valued mapping that the value space is a partially ordered topological vector space which the order is induced by cone but not a Dedeking complete vector space.

关 键 词：基础数学 泛函分析 序拓扑向量空间 集值映射 锥一凸 上(下)半连续 

分 类 号：O177.32[理学—数学]