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Directed Completions of Local Dcpos(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2017年04期
Page:
1-
Research Field:
·数学与计算机科学·
Publishing date:

Info

Title:
Directed Completions of Local Dcpos
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)
Keywords:
local dcpo; directed completion; continuous local dcpo
PACS:
O189.1; O153.1
DOI:
10.3969/j.issn.1001-4616.2017.04.001
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.

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.

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Last Update: 2017-12-30