Extensions of Set-valued Mapping on Partially Ordered Vector Spaces
Xiao Yun · Journal of Chengdu University of Information Technology · 2011
The extension and popularizaton theorems of classical Hahn-Banach have been applied very widely,but focus the discuss on the expansion of single valued mapping.In order to discuss the expansion of multiple valued mapping further,based on constructing the subspace and use the Zorn lemma in this paper,we obtained that extension theorem concerning the set valued mapping from a vector space into a Dedekind complete partially ordered vector space which the order is induced by cone.At the same time,the extension theorem that the continue set valued mapping from a vector space into a topological vector space was obtained.The results not only popularized the Hahn-Banach extension theorem further but aslo extend the application.