QFS-Domains and their Lawson Compactness

被引:9
作者
Li, Gaolin [1 ,2 ]
Xu, Luoshan [1 ]
机构
[1] Yangzhou Univ, Dept Math, Yangzhou 225002, Peoples R China
[2] Yancheng Teachers Coll, Dept Math, Yancheng 224002, Peoples R China
来源
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2013年 / 30卷 / 01期
关键词
Quasi-finitely separating map; Quasi-approximate identity; QFS-domain; Quasicontinuous domain; Lawson compactness; FS-DOMAINS; POSETS; SPACES;
D O I
10.1007/s11083-011-9238-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, concepts of quasi-finitely separating maps and quasi-approximate identities are introduced. Based on these concepts, QFS-domains and quasicontinuous maps are defined. Properties and characterizations of QFS-domains are explored. Main results are: (1) finite products, nonempty Scott closed subsets and quasicontinuous projection images of QFS-domains, as well as FS-domains, are all QFS-domains; (2) QFS-domains are compact in the Lawson topology; (3) An L-domain is a QFS-domain iff it is an FS-domain, iff it is compact in the Lawson topology; (4) Bounded complete quasicontinuous domains, in particular quasicontinuous lattices, are all QFS-domains.
引用
收藏
页码:233 / 248
页数:16
相关论文
共 14 条
[1]  
Abramsky Samson., 1994, Domain theory
[2]  
Engelking R., 1997, GEN TOPOLOGY
[3]   GENERALIZED CONTINUOUS AND HYPERCONTINUOUS LATTICES [J].
GIERZ, G ;
LAWSON, JD .
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1981, 11 (02) :271-296
[4]  
GIERZ G, 1983, HOUSTON J MATH, V9, P191
[5]  
Gierz G., 2003, Continuous Lattices and Domains
[6]   Characterising FS domains by means of power domains [J].
Heckmann, R .
THEORETICAL COMPUTER SCIENCE, 2001, 264 (02) :195-203
[7]  
Jung A., 1990, Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science (90CH2897-7), P35, DOI 10.1109/LICS.1990.113731
[8]  
Jung A., 1989, CWI TRACTS, V66
[9]   Metric spaces and FS-domains [J].
Lawson, Jimmie D. .
THEORETICAL COMPUTER SCIENCE, 2008, 405 (1-2) :73-74
[10]  
[李高林 LI Gaolin], 2007, [模糊系统与数学, Fuzzy Systems and Mathematics], V21, P52