关于Lowen空间指数对象的一点注记  

A NOTE ON EXPONENTIAL LOWEN SPACES

作　　者：刘应明[1] 张德学[1] 

机构地区：[1]四川大学数学系,成都610064

出　　处：《数学年刊（A辑）》2002年第1期33-40,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19831040;No.10071053);四川省青年科技基金(No.457)资助的项目.

摘　　要：Ｌ－拓扑空间（Ｘ，△）称为一 Ｌｏｗｅｎ空间若△有一组由层特征函数构成的基，即△中形如ａ∧Ｕ，ａ∈Ｌ，Ｕ　Ｘ的元素构成△的一组基．若Ｌ＝［０，１］；则（Ｘ，△）是一Ｌｏｗｅｎ空间当且仅当（Ｘ，△）是一 Ｌｏｗｅｎ意义下的ｆｕｚｚｙ邻域空间．通过在函数空间上引入适当的Ｌ－拓扑结构，证明了若０∈Ｌ是一素元并且Ｌｏｗｅｎ空间（Ｘ，△）的开集格是一连续格，则（Ｘ，△）是Ｌｏｗｅｎ空间范畴中一指数对象．特别地，若一ｆｕｚｚｙ邻域空间的开集格连续，则它是ＦＮＳ中一指数对象．An L-topological space (X,△) is called a Lowen space if △ has a basis consisting of leveled characteristic functions, that is to say, the elements in △ of the form a ∧ U, a∈L,U X, is a basis for △. In the case L = [0,1], (X, △) is a Lowen space if and only if (X, △) is a fuzzy neighborhood space in the sense of Lowen. By introducing some natural L-topologies for function spaces it is proved in this paper that if 0 ∈ L is a prime then a Lowen space (X, △) is exponential in the category of Lowen spaces provided that its open-set lattice is continuous. Particularly a fuzzy neighbourhood space is exponential in FNS if its open-set lattice is continuous.

关 键 词：L-拓扑空间 Lowen空间 指数对象 完全分配格 Fuzzy领域空间 

分 类 号：O189.1[理学—数学]