交连续dcpo的遗传性和不变性  

Heredity and Invariance of Meet Continuous Dcpos

作　　者：戴向梅[1,2] 徐罗山[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002 [2]东台中学数学组,江苏东台224200

出　　处：《模糊系统与数学》2010年第3期76-81,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10371106;60774073)

摘　　要：讨论了交连续dcpo的遗传性和不变性,证明了如下结论:(1)交连续dcpo对于开子空间和闭子空间都是可遗传的;(2)交连续dcpo在加最大元和去最小元运算下保持交连续性;(3)交连续dcpo的收缩核为交连续dcpo。另外,给出了交连续的主理想刻画的一个直接证明;构造了反例说明交连续dcpo对于主滤子是不可遗传的;也构造了反例说明所有主滤子都交连续的一个dcpo,自身不必是交连续的。In this paper, heredity and invariance of meet continuous dcpos are discussed. Main results are： （1） Meet continuous dcpos are hereditary for Scott open or closed subsets; （2） A dcpo obtained by adding a top element or a bottom element to a meet continuous dcpo remains a meet continuous dcpo; （3） Retractions of meet continuous dcpos are all meet continuous dcpos. In adition, a direct proof for the characterization theorem of meet continuity with pricipal ideals is given. Some counterexamples are constructed to show that meet continuous dcpos are not hereditary for principal filters and to show that a dcpo may not be meet continuous even with each principal filter being meet continuous dcpo.

关 键 词：交连续dcpo SCOTT拓扑 主理想 主滤子 子空间 

分 类 号：O153[理学—数学]