摘要
引入了相容连续偏序集及其定向完备化等概念 ,证明了相容连续偏序集的定向完备化是连续偏序集 ;利用主理想及 Scott拓扑刻画了相容连续偏序集 ,得到相容定向完备偏序集是相容连续的当且仅当它的任一主理想是连续偏序集也当且仅当它的 Scott拓扑是一个完全分配格 ;考察了相容连续偏序集的定向完备化的范畴意义 ,得到相容连续偏序集范畴以连续偏序集范畴作为满的反射子范畴 .
This paperintroduces the new concepts of consistently continuousposetsand theirdirect- ed completions. It is proved that the completion of a consistently continuous poset is a continuous poset;Itis obtained that a directed complete poset is a consistently continuous posetif and only if its principal ideals are all continuous posets,and if and only if its Scotttopology is completely com- plete distributive. With the directed completion,it is also showed that the category of continuous posets is a full reflective subcategory of consistently continuous posets.
出处
《扬州大学学报（自然科学版）》
CAS
CSCD
2000年第1期1-6,10,共7页
Journal of Yangzhou University：Natural Science Edition
基金
国家教委留学回国人员基金资助项目
