| Fuzzy线性泛函的连续性与Hahn-Banach定理的Fuzzy推广 |
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| 引用本文： | 方锦暄,严从华.Fuzzy线性泛函的连续性与Hahn-Banach定理的Fuzzy推广[J].南京师大学报,1990(3). |
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| 作者姓名： | 方锦暄 严从华 |
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| 作者单位： | 南京师大数学系
(方锦暄)，南京师大数学系(严从华) |
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| 基金项目： | 江苏省教委自然科学基金 |
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| 摘 要： | 本文采用1]中fuzzy线性泛函的定义,证明了fuzzy拓扑线性空间上fuzzy线性泛函连续性的几个等价命题和fuzzy线性泛函的Hahn-Banach延拓定理。给出了fuzzy拓扑线性空间上存在非零连续fuzzy线性泛函的一个充要条件,并证明了非平几的分离的局部凸fuzzy拓扑线性空间上存在足够多的非零连续fuzzy线性泛函。
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| 关 键 词： | Fuzzy拓扑线性空间 局部凸fuzzy拓扑线性空间 fuzzy线性泛函 连续的fuzzy线性泛函 Hahn-Banach延拓定理 |
CONTINUITY OF FUZZY LINEAR FUNCTIONAL AND FUZZY GENERALIZATION OF HAHN-BANACH THEOREM |
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| Fang Jinxuan Yah Chonghua.CONTINUITY OF FUZZY LINEAR FUNCTIONAL AND FUZZY GENERALIZATION OF HAHN-BANACH THEOREM[J].Journal of Nanjing Normal University(Natural Science Edition),1990(3). |
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| Authors: | Fang Jinxuan Yah Chonghua |
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| Institution: | Department of Mathematics |
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| Abstract: | In this per, the definition of fuzzy linear functional which was given in 1] is adopted. We prove the seceral equivalent propositions for continuity of fuzzy linear functional on fuzzy topologicallinear space and Hahn-Banach extension theorem of fuzzy linear functional. We also give a sufficient and necessary condition that ensures there exist non-zero continuous fuzzy linear functionals on a fuzzy topological linear space, and prove that there exist enough non-zero continuous fuzzy linear functionals on non-zero separate locally convez fuzzy topological linear space, |
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| Keywords: | Fuzzy topological linear space locally convex fuzzy topological linear space fuzzy linear functional continuous fuzzy linear functional Hahn-Banach extension theorem |
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