| 线性Fuzzy邻域空间中的层次结构 |
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| 引用本文： | 李三江,罗懋康.线性Fuzzy邻域空间中的层次结构[J].四川大学学报(自然科学版),2001,38(2):141-145. |
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| 作者姓名： | 李三江 罗懋康 |
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| 作者单位： | 四川大学数学学院, |
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| 基金项目： | 国家自然科学基金、教育部博士点基金和教育部"跨世纪优秀人才培养计划"基金 |
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| 摘 要： | 作者讨论了线性Fuzzy邻域空间中的层次结构,得到以下结果：⑴线性Fuzzy邻域空间（X,△）局部n-凸当且仅当其各层拓扑线性空间局部凸;⑵线性Fuzzy邻域空间（X,△）是（QL）型Fuzzy拓扑线性空间当且仅当其为诱导空间。
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| 关 键 词： | Fuzzy拓扑线性空间 线性Fuzzy邻域空间 （QL）型Fuzzy拓扑线性空间 局部n－凸 层次结构 诱导空间 局部凸 |
| 文章编号： | 0490-6756(2001)02-0l41-05 |
ON LEVEL-STRUCTURE IN LINEAR FUZZY NEIGHBOURHOOD SPACES |
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| LI San-jiang,LUO Mao-kang.ON LEVEL-STRUCTURE IN LINEAR FUZZY NEIGHBOURHOOD SPACES[J].Journal of Sichuan University (Natural Science Edition),2001,38(2):141-145. |
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| Authors: | LI San-jiang LUO Mao-kang |
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| Abstract: | The authors discuss the level-structure in linear Fuzzy neighbourhood spaces which was introduced by A.K. Katsaras(A. K. Katsaras,Linear Fuzzy neighborhood spaces, Fuzzy sets and systems 16(1985) 25～ 40). The authors get the following results: (1) linear Fuzzy neighbourhood space (X,N) is locally n-convex if and only if each of its a-level space ( X, a ( t (N) ) is locally convex; (2) linear Fuzzy neighbourhood space ( X, N) is (QL)-type Fuzzy topological linear space(C. X. Wu,J. X. Fang, (QL)-type Fuzzy topological space, Chinese Annals of Math., 6A(3 ): 355～364) if and only if it is topologically generated (or, another word, is induced). |
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| Keywords: | Fuzzy topological linear space Fuzzy neighbourhood space linear Fuzzy neighbourhood space (QL)-type Fuzzy topological linear space locally n-convex |
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