连续poset的投射像的连续性  

Continuity of Projection Images of Continuous Posets

作　　者：徐罗山[1] 栾云骏 

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》2014年第2期91-94,共4页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61074129;61103018;11101352);江苏省自然科学基金资助项目(BK2010313;BK2011442);国家重点实验室开放课题(SKLSDE-2011KF-08)

摘　　要：本文用反例说明了连续poset的保定向并的投射像不必连续,指出了《Continuous Lattices and Domains》一书中定理I-2.2的错误.证明了连续poset在保定向并的核映射下的像和连续收缩核还是连续的。In this paper, a counterexample is constructed to show that projection images of continuous posets needn＇t be continuous, indicating that Theorem I-2. 2 in the book ＂Continuous Lattices and Domains＂ is not true for posers. It is proved that images of continuous posers under kernel operators, or retractions preserving directed sups are still continuous posets.

关 键 词：连续poset 投射像 定向并 收缩核 

分 类 号：O153[理学—数学] O189[理学—基础数学]