[1]徐爱军,贺 伟.局部定向完备集的定向完备化（英文）[J].南京师范大学学报(自然科学版),2017,40(04):1.[doi:10.3969/j.issn.1001-4616.2017.04.001]
　Xu Aijun,He Wei.Directed Completions of Local Dcpos[J].Journal of Nanjing Normal University(Natural Science Edition),2017,40(04):1.[doi:10.3969/j.issn.1001-4616.2017.04.001]
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局部定向完备集的定向完备化（英文）()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第40卷
期数:
2017年04期
页码:
1
栏目:
·数学与计算机科学·
出版日期:
2017-12-30

文章信息/Info

Title:
Directed Completions of Local Dcpos
文章编号:
1001-4616(2017)04-0001-06
作者:
徐爱军1; 贺 伟2
(1.南京林业大学应用数学系,江苏 南京 210037)(2.南京师范大学数学科学学院,江苏 南京 210046)
Author(s):
Xu Aijun1; He Wei2
(1.Department of Applied Mathematics,Nanjing Forestry University,Nanjing 210037,China)(2.School of Mathematical Sciences,Nanjing Normal University,Nanjing 210046,China)
关键词:
局部定向完备集; 定向完备化; 连续的局部定向完备集
Keywords:
local dcpo; directed completion; continuous local dcpo
分类号:
O189.1; O153.1
DOI:
10.3969/j.issn.1001-4616.2017.04.001
文献标志码:
A
摘要:
研究了局部定向完备集的定向完备化,得出以下两个结果:(1)连续(代数)的局部定向完备集的定向完备化是连续(代数)定向完备集;(2)连续(代数)定向完备集范畴是连续(代数)局部定向完备集范畴的满的反射子范畴.
Abstract:
In this paper,we explore directed completions of local dcpos. The following results are obtained.(1)The directed completions of continuous(resp.,algebraic)local dcpos are continuous(resp.,algebraic)dcpos;(2)The category CDcpo(resp.,ADcpo)of continuous(resp.,algebraic)dcpos and Scott continuous maps is a full reflective subcategory of the category CLDcpo(resp.,ALDcpo)of continuous(resp.,algebraic)local dcpos and local Scott continuous maps.

参考文献/References:

[1] XU L S. Consistent continuous poset and their directed completions[J]. J of Yangzhou university(nature science edition),2000,3(1):1-6.
[2]GUAN X C,WANG G P. A kind of local directed complete sets and properties of the categories[J]. Advances in mathematics,2005,34(6):677-682.
[3]XU A J,WANG G P. Cartesian closeness of the categories of algbraic local complete posets and FS-local directed complete posets[J]. Advances in mathematics,2006,35(4):485-492.[4]GIREZ G,HOFMANN K H,KEIMEL K,et al. Continuous lattics and domains[M]. Cambridge:Cambridge University Press,2003. [5]He W. Category theory[M]. Beijing:Science Press,2006.

备注/Memo

备注/Memo:
Received data:2016-11-17.
Foundation item:Supported by the National Natural Science Foundation of China(2012101GZ30060),the Nanjing Forestry University with High Academic Qualifications Fund(163101088).?
Corresponding author:Xu Aijun,Ph.D.,associate professor,majored in topology. E-mail:ajxu@njfu.edu.cn
更新日期/Last Update: 2017-12-30