Z-半连续格  

Z-Semicontinuous Lattice

作　　者：张文锋[1] 徐晓泉[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《模糊系统与数学》2012年第3期148-155,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10861007;11161023);高等学校全国优秀博士学位论文作者专项资金资助项目(2007B14);江西省自然科学基金资助项目(2007GZS179;20114BAB201008);江西省教育厅科技基金资助项目(GJJ12657);江西省研究生创新专项基金资助项目(YC09A054)

摘　　要：作为连续格和半连续格的公共推广,引入了广义理想子系统Z、Z-半连续格及强Z-连续格的概念,讨论了它们的基本性质和Z-半连续格的函数空间的结构,给出了强Z-连续格到方体的嵌入,证明了当子系统Z满足一定条件时,Z-半连续格范畴SCLZ是笛卡儿闭的。As a common generalization of continuous lattice and semicontinuous lattices, the concepts of generalized ideal sub-systems, Z-semicontinuous and strongly Z-continuous lattices are introduced, and some basic properties and the structures of function spaces on Z-semicontinuous lattices and strongly Z-continuous lattices are investigated, and an embedding theorem for strongly Z-continuous lattices into a cube is given. It is proved that category SCLz on Z-semicontinuous lattices is Cartesian closedness when it satisfies certain conditions.

关 键 词：广义理想子系统 Z-半连续格 强Z-连续格 Z-半Scott拓扑 函数空间 

分 类 号：O159[理学—数学]