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

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.