广义模糊赋范空间中的模糊闭集和模糊开集

J4 ›› 2011, Vol. 46 ›› Issue (4): 113-117.

广义模糊赋范空间中的模糊闭集和模糊开集

杨萍,曹怀信*,司海燕

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2010-10-28 发布日期:2011-04-21
通讯作者: 曹怀信(1958- ), 男, 教授, 博士生导师, 主要从事算子理论与量子计算领域的研究. Email: caohx@snnu.edu.cn
作者简介:杨萍(1986- ), 女, 硕士研究生, 主要从事算子理论的研究. Email: yangping0604@163.com
基金资助:
国家自然科学基金资助项目(10571113, 10871224)

Fuzzy closed and fuzzy open sets in a generalized fuzzy normed space

YANG Ping, CAO Huai-xin*, SI Hai-yan

College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China

Received:2010-10-28 Published:2011-04-21

摘要/Abstract

摘要：

介绍了模糊开(闭)球并证明了它们的一些性质。定义了模糊开(闭)集,由此诱导了广义模糊赋范空间上的一个拓扑。最后,借助广义模糊赋范空间中模糊闭球套的概念,证明了有关完备广义模糊赋范空间的两个结论。

关键词: 广义模糊赋范空间;模糊收敛性;模糊有界性;模糊闭球套

Abstract:

The definitions of fuzzy open ball and fuzzy closed ball are introduced and some properties of them are proved. Then fuzzy open and fuzzy closed sets are defined which can induced a topology on a generalized fuzzy normed space (X,N,*). Finally two conclusions of a complete generalized fuzzy normed space are proved by the concept of nest of fuzzy closed balls in a generalized fuzzy normed space.

Key words: generalized fuzzy normed space; fuzzy convergence; fuzzy boundedness; nest of fuzzy closed balls

杨萍,曹怀信*,司海燕. 广义模糊赋范空间中的模糊闭集和模糊开集[J]. J4, 2011, 46(4): 113-117.

YANG Ping, CAO Huai-xin*, SI Hai-yan. Fuzzy closed and fuzzy open sets in a generalized fuzzy normed space[J]. J4, 2011, 46(4): 113-117.

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