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.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
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)
