| 半连续dcpo |
| |
| 引用本文： | 刘玉连,李高林,徐罗山.半连续dcpo[J].扬州大学学报(自然科学版),2012,15(2):1-5. |
| |
| 作者姓名： | 刘玉连 李高林 徐罗山 |
| |
| 作者单位： | 1. 扬州大学数学科学学院,江苏扬州,225002
2. 扬州大学数学科学学院,江苏扬州225002;盐城师范学院数学科学学院,江苏盐城224002 |
| |
| 基金项目： | 国家自然科学基金资助项目，江苏省自然科学基金资助项目，国家重点实验室开放课题，盐城师范学院资助项目 |
| |
| 摘 要： | 作为半连续格的推广,引入半素集和半连续dcpo的概念,并讨论半连续dcpo的性质,在半连续dcpo中得到类似于半连续格的一些主要结果.同时研究了dcpo的内蕴拓扑——半Scott拓扑、半Lawson拓扑,证明了上集U半Lawson开当且仅当U为半Scott开,下集U半Lawson闭当且仅当U为半Scott闭.最后研究了半连续映射,证明了若保序映射f半连续,则f关于半Scott拓扑是连续映射.
|
| 关 键 词： | 半素集 半连续dcpo 半Scott拓扑 半连续映射 |
Semicontinuous dcpos |
| |
| LIU Yu-lian
,
LI Gao-lin
,
XU Luo-shan.Semicontinuous dcpos[J].Journal of Yangzhou University(Natural Science Edition),2012,15(2):1-5. |
| |
| Authors: | LIU Yu-lian LI Gao-lin XU Luo-shan |
| |
| Institution: | 1(1.Sch of Math Sci,Yangzhou Univ,Yangzhou 225002,China; 2.Sch of Math Sci,Yancheng Teachers’ Coll,Yancheng 224002,China) |
| |
| Abstract: | As a generalization of semicontinuous lattices,the concepts of semiprime sets and semicontinuous dcpos are introduced.Basic properties of semicontinuous dcpos are discussed.The main results of the theory of semicontinuous lattices are carried to semicontinuous dcpo.Moreover,some intrinsic topologies—the semi-Scott topology and the semi-Lawson topology on semicontinuous dcpos are investigated.It is proved that an upper set U is semi-Lawson open iff it is semi-Scott open;a lower set U is semi-Lawson closed iff it is semi-Scott closed.Finally the concept of semicontinuous mapping is introduced,it is showed that if f is order preserving and semicontinuous,then f is continuous with respect to the semi-Scott topologies. |
| |
| Keywords: | semi-prime set semicontinuous dcpo semi-Scott topology semicontinous mapping |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
