C-连续偏序集的性质及等价刻画  

Properties and Characterizations of C-continuous Posets

作　　者：何青玉[1] 徐罗山[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《模糊系统与数学》2015年第3期8-12,共5页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金项目(61103018;61300153);江苏省研究生创新工程项目(CXLX12-0905)

摘　　要：在偏序集上考察了C-连续性,并引入了主理想C-连续的概念。利用提升和主理想C-连续等概念给出了C-连续性的两个等价刻划。证明了交半格C-连续当且仅当它是主理想C-连续的。构造了反例说明偏序集的C-连续性与主理想C-连续性互不蕴涵。In this paper, C-continuity on posets is studied. The concept of principal ideal C-continuity for posets is introduced. By the lifting method and principal ideal C-continuity, two new characterizations for C-continuous posets are given. It is proved that C-continuity is equivalent to the principal ideal C-continuity on semilattices. Two counterexamples are constructed to show that C-continuity and the principal ideal C-continuity on posets can not imply each other.

关 键 词：C-逼近关系 C-连续偏序集 主理想C-连续 Scott拓扑下可遗传 

分 类 号：O153[理学—数学] O189[理学—基础数学]