| FS-相容Domain的定向完备化及相关范畴性质 |
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| 引用本文： | 王习娟,徐罗山.FS-相容Domain的定向完备化及相关范畴性质[J].模糊系统与数学,2005,19(3):82-87. |
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| 作者姓名： | 王习娟 徐罗山 |
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| 作者单位： | 1. 连云港师范专科学校,数学系,江苏,连云港,222006
2. 扬州大学,数学科学学院,江苏扬州,225002 |
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| 基金项目： | 国家自然科学基金资助项目（10371106,10410638）;江苏省教育厅指导性计划资助项目（FK0310060） |
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| 摘 要： | 引入FS-相容Domain概念，研究FS-相容Domain的性质，主要结果有：（1）FS-相容Domain的收缩核与连续函数空间还是FS-相容Domain；（2）FS-相容Domain是有限生成上集，从而是Scott紧的；（3）FS-相容Domain的定向完备化是FS-Domaln；（4）有最大元的FS-Domain去掉最大元后是FS-相容Domain；（5）证明了以Scott连续映射为态射，FS-相容Domain为对象的范畴FS-CDOM是笛卡儿闭范畴并以FS-Domain范畴FS-DOM作为满的反射子范畴。
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| 关 键 词： | FS-相容Domain 定向完备化Scott拓扑 笛卡儿闭范畴 |
| 文章编号： | 1001-7402（2005）03-0082-06 |
| 收稿时间： | 2004-03-18 |
| 修稿时间： | 2004-06-11 |
Directed Completions of Consistent FS-domains and Related Categorical Properties |
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| WANG Xi-juan,XU Luo-shan.Directed Completions of Consistent FS-domains and Related Categorical Properties[J].Fuzzy Systems and Mathematics,2005,19(3):82-87. |
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| Authors: | WANG Xi-juan XU Luo-shan |
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| Abstract: | The new concept of consistent FS-domains is introduced. Some basic properties of consis- tent FS-domains are given. The following are the main obtained results: (1) Retracts and continuous function spaces of consistent FS-domains are consistent FS-domains; (2) Consistent FS-domains are all finitely upper generated and Scott compact; (3) Directed completions of consistent FS-domains are FS-domains; (4) If L is an FS-domain with a top 1, then L\\{1} is a consistent FS-domain; (5) The category FS-CDOM of consistent FS-domains and Scott continuous functions is Cartesian closed and has the category FS-DOM of FS-domains and Scott continuous functions as a full reflective subcategory. |
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| Keywords: | Consistent FS-Domain Directed Completion Scott Topology~ Cartesian Closed Category |
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