偏序集的φ-(交)连续性及其主理想刻画  

φ-(Meet) Continuity on Posets and Their Characterizations by Principal Ideals

作　　者：毛徐新[1] 徐罗山[2] 

机构地区：[1]南京大学数学系,江苏南京210093 [2]扬州大学数学科学学院,江苏扬州225002

出　　处：《模糊系统与数学》2005年第4期103-108,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(1037110610410638);江苏省教育厅指导项目(FK0310060)

摘　　要：证明φ-完备偏序集是(强)φ-连续的当且仅当该偏序集的任一主理想是(强)φ-连续的。在φ-完备偏序集中利用φ-S集族生成-φS cott拓扑,并由此引入φ-交连续偏序集概念。证明φ-完备偏序集是φ-交连续的当且仅当该偏序集的任一主理想是φ-交连续的。It is proved that a φ-complete poset is （strong） φ-continuous if and only if each principal ideal is （strong） φ-continuous. With the concept of φ-S sets in a φ-complete poset,the φ-Scott topology on a φ-complete poset is defined. Meanwhile, the new concept of φ-meet continuous posets is introduced and it is proved that a φ-complete poset is φ-meet continuous iff each principal ideal is φ-meet continuous.

关 键 词：φ-连续偏序集 主理想 φ-Scott拓扑 φ-交连续偏序集 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]