Quantale中的L-模糊滤子及其相关性质-陕西师范大学学报期刊社网站

陕西师范大学学报（自然科学版）

数学与计算机科学

Quantale中的L-模糊滤子及其相关性质

单晓伟, 刘妮*

（陕西师范大学数学与信息科学学院，陕西西安 710062）

单晓伟,女,硕士研究生,研究方向为格上拓扑学. E-mail: shan201011@163.com.*通信作者: 刘妮,女,副教授,博士.E-mail: niliu@snnu.edu.cn.

摘要:

基于完备格L,在Quantale中引入了L-模糊滤子的概念,并研究了L-模糊滤子的基本性质.在L是闭集格的条件下,得到了Quantale中的L-模糊滤子的等价刻画;在L是空间式Frame且Q是幂等左半可换Quantale的条件下,证明了LQ上的生成滤子映射是Quantale核映射,进而全体L-模糊滤子构成的Quantale FilL(Q)是LQ的幂等的商Quantale;在Quantale中定义了L-模糊滤子拓扑,并得到了Quantale同态关于相应的L-模糊滤子拓扑连续的结论.

关键词：

Quantale; L-模糊滤子; L-模糊滤子拓扑; 商Quantale; 连续映射

收稿日期：

2012-08-27

中图分类号：

O153.1

文献标识码：

文章编号：

1672-4291(2013)02-0014-05

基金项目：

国家自然科学基金资助项目(11001158);中央高校基本科研业务费专项资金项目(GK201002025).

Doi:

L-fuzzy filters of Quantales and their related properties

SHAN Xiao-wei, LIU Ni*

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

Abstract:

Based on a complete lattice L, the concept of L-fuzzy filter in Quantales is introduced and its related properties are studied.When L is a closed-set lattice, the equivalent characterizations of L-fuzzy filters are given. It is proved that the generated filter mapping of LQ is a quantic nucleus and the Quantale FilL(Q) consisting of all L-fuzzy filters is the idempotent quantic quotient of LQ when L is a spatial Frame and Q is an idempotent left semi-communicative Quantale. Finally,L-fuzzy filter topology on a Quantale is defined and it is obtained that a Quantale homomorphism is continuous with respect to the corresponding L-fuzzy filter topology.

KeyWords:

Quantale; L-fuzzy filter; L-fuzzy filter topology; quantic quotient; continuous mapping