On linearly topological structure and property of fuzzy normed linear space

Jianzhong Xiao; Xinghua Zhu

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On linearly topological structure and property of fuzzy normed linear space

机译：模糊赋范线性空间的线性拓扑结构和性质

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In this paper, the simplified definition of fuzzy normed linear space is introduced; the different structure of fuzzy normed linear space with variable right norm R is discussed in terms of topological vector space, and its properties such as compactness, completeness and density are studied under more general left norm L and right norm R; as application, the linearly topological structure of Menger PN space is obtained.

机译：本文介绍了模糊赋范线性空间的简化定义。从拓扑向量空间的角度讨论了具有可变右范数R的模糊范线性空间的不同结构，并在更一般的左范数L和右范数R下研究了其紧性，完整性和密度等性质。作为应用，得到了Menger PN空间的线性拓扑结构。

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来源
《Fuzzy sets and systems》 |2002年第2期|p.153-161|共9页
作者
Jianzhong Xiao; Xinghua Zhu;
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作者单位

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类模糊数学;
关键词
Fuzzy topology; Fuzzy functional analysis; Fuzzy normed linear space; Fuzzy norm;

机译：模糊拓扑;模糊功能分析;模糊范数线性空间;模糊范数;

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1. Fuzzy normed linear space and its topological structure [J] . I. Sadeqi, F. Solaty Kia Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2009,第5期

机译：模糊赋范线性空间及其拓扑结构
2. Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and its Fuzzy Compactness [J] . Mami Sharma, Debajit Hazarika New Mathematics and Natural Computation . 2020,第1期

机译：模糊界线线性运算符在模糊规范的线性空间及其模糊致密度
3. Fuzzy bounded linear operators in Felbin's type fuzzy normed linear spaces [J] . T. Bag, S.K. Samanta Fuzzy sets and systems . 2008,第6期

机译：Felbin型模糊赋范线性空间中的模糊有界线性算子
4. Some properties of fuzzy bounded sets in fuzzy normed linear spaces [C] . Alexandru Szabo, Tudor Binzar, Sorin Nadaban, International Conference of Numerical Analysis and Applied Mathematics . 2018

机译：模糊规范线性空间中模糊界定集的一些特性
5. Invariant subspace problem and spectral properties of bounded linear operators on Banach spaces, Banach lattices, and topological vector spaces [D] . Troitsky, Vladimir G. 1999

机译：Banach空间，Banach格和拓扑矢量空间上有界线性算子的不变子空间问题和谱性质
6. Some Properties of Real Linear Topological Spaces [O] . D. G. Bourgin 1941

机译：实线性拓扑空间的一些性质
7. On some topological properties of intuitionistic 2-fuzzy n-normed linear spaces [O] . Lj.D.R. Kocinac, V.A. Khan, K.M.A.S. Alshlool, 2019

机译：关于直觉2-FIZY N规范线性空间的一些拓扑特性
8. Admissibility, Homeomorphism Extension and the AR-Property in Topological Linear Spaces [R] . van der Bijl, J., Dobrowolski, T., Hart, K. P., 1991

机译：可拓性，同胚扩展和拓扑线性空间中的aR-性质

On linearly topological structure and property of fuzzy normed linear space

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