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

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.