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偏序集和连续偏序集上的Scott拓扑(英文)
The Scott Topology on Posets and Continuous Posets

范丽红;贺伟;
FAN Lihong~

南京师范大学数学与计算机科学学院;台州学院数学与信息工程学院;
(1,2,*),HE Wei~(1,**) (1.School of Mathematics and Computer Science,Nanjing Normal University,Nanjing,Jiangsu, 210097,P.R.China;2.School of Mathematics and Information Engineering,Taizhou University, Taizhou,Zhejiang,317000,P.R.China

收稿日期: 2009-12-25
出版日期: 2009-12-25

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摘要 本文以S-极限的方式在任意偏序集上定义了Scott拓扑,这推广了定义在dcpo上的Scott拓扑.给出了偏序集或连续偏序集上的Scott拓扑的一些性质.还证明了偏序集范畴不是Cartesian闭的,因此FS-偏序集范畴和B-偏序集范畴也不是Cartesian闭的.作为推论,指出了相容定向完备偏序集范畴CDCPO是偏序集范畴POSET的Cartesian闭的满子范畴.
关键词 连续偏序集Scott拓扑相容定向完备偏序集Cartesian闭范畴    
Abstract:In this paper,we define the Scott topology on arbitrary poset by means of S-limit,which extends the Scott topology defined on a dcpo.We will show that the Scott topology defined on a poset or a continuous poset has many similar properties to those of the Scott topology defined on a dcpo or a domain.We also show that the category POSET of posets and Scott continuous maps is not Cartesian closed,thus the categories of FS-posets and B-posets are not Cartesian closed.As a corollary,we show that the category CDCPO of consistent directed complete posets(in short,cdcpos) and Scott continuous maps is a Cartesian closed full subcategory of POSET.
Key wordsScott topology    consistent directed complete posets    Cartesian closed category
[1] 李庆国;李纪波;. 基于下极限收敛的偏序集的交连续性(英文)[J]. 数学进展, 2010, 39(6): 755-760.
[2] 王习娟;卢涛;贺伟;. 关于连续偏序集的一个刻画定理(英文)[J]. 数学进展, 2010, 39(1): 95-98.
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