| 偏序向量空间中集值映射的一类扩张定理 |
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| 引用本文： | 肖赟.偏序向量空间中集值映射的一类扩张定理[J].成都信息工程学院学报,2011,26(3):338-342. |
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| 作者姓名： | 肖赟 |
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| 作者单位： | 宜宾学院数学学院,四川宜宾,644000 |
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| 摘 要： | 经典的Hahn-Banach扩张定理及其推广定理有着非常广泛的应用,但主要都是讨论单值映射的扩张性质。为了进一步讨论多值映射的扩张性质,通过构造的方法,利用了zorn引理及偏序向量空间的完备性,得到了当定义域空间是一个实向量空间,而值域空间是由锥引入序的Dedekind完备的偏序向量空间时集值映射的一类扩张性质,以及当给值域空间引入相应拓扑时连续集值映射的一类扩张性质。其结果进一步推广了Hahn-Banach扩张定理,扩大了其应用范围。
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| 关 键 词： | 基础数学 泛函分析 偏序向量空间 集值映射 扩张定理 上(下)半连续 |
Extensions of Set-valued Mapping on Partially Ordered Vector Spaces |
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| XIAO Yun.Extensions of Set-valued Mapping on Partially Ordered Vector Spaces[J].Journal of Chengdu University of Information Technology,2011,26(3):338-342. |
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| Authors: | XIAO Yun |
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| Institution: | XIAO Yun(Department of Mathematics YiBin University,YiBin 644000,China) |
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| Abstract: | The extension and popularizaton theorems of classical Hahn-Banach have been applied very widely, but fo- cus the discuss on the expansion of single valued mapping. In order to discuss the expansion of multiple valued map- ping 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. |
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| Keywords: | fundamental mathematics functional analysis partially ordered vector spaces extension theorem set valued mapping upper（lower）-continuous |
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