WZ-Domain与WZ-Scott拓扑  

WZ-Domain and WZ-Scott Topology

作　　者：刘敏[1] 赵彬[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：《模糊系统与数学》2010年第2期50-56,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10871121)

摘　　要：引入WZ-双小于关系,以此为基础给出WZ-Domain的概念,讨论它的基本性质,证明当子集系统Z满足一定条件时,WZ-Domain上的WZ-双小于关系具有插入性。其次,在Z-完备偏序集上定义WZ-Scott拓扑,证明在一定条件下一个映射关于该拓扑是连续映射当且仅当该映射保定向的Z集之并。最后对WZ-Domain上的WZ-Scott拓扑的性质进行研究,证明对一类子集系统,WZ-Scott拓扑空间是Sober空间当且仅当该拓扑空间具有Rudin性质。Firstly, the WZ-way below relation is defined and based on it, the concept of WZ-Domain is introduced. It is proved that if a subset system Z satisfies certain conditions and P is a WZ-Domain, then the WZ-way below relation on P has the interpolation property. Secondly, we introduced the concept of WZ-Scott topology. It is proved that under certain conditions a function is continuous with respect to this topology if and only if it preserves the suprema of Z-sets that are directed. Finally, some properties about the WZ-Scott topology of WZ-Domains are investigated.

关 键 词：子集系统 WZ-双小于关系 WZ—Domain WZ—Scott拓扑 

分 类 号：O153[理学—数学]