Quantale中的L-模糊滤子及其相关性质  

L-fuzzy filters of Quantales and their related properties

作　　者：单晓伟[1] 刘妮[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2013年第2期14-18,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：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)

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.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.

关 键 词：QUANTALE L-模糊滤子 L-模糊滤子拓扑 商Quantale 连续映射 

分 类 号：O153.1[理学—数学]