| 连续偏序集及其Smyth幂的特征与浓度 |
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| 引用本文： | 刘海玉,徐罗山. 连续偏序集及其Smyth幂的特征与浓度[J]. 徐州师范大学学报(自然科学版), 2006, 24(1): 6-10 |
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| 作者姓名： | 刘海玉 徐罗山 |
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| 作者单位： | 1. 徐州师范大学,数学系,江苏,徐州,221116;江苏技术师范学院,基础部,江苏,常州,213001
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(1037110610410638)，江苏省教育厅自然科学基金资助项目(FK0310060) |
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| 摘 要： | 推广连续domain的特征与浓度的概念到连续偏序集上,探讨了连续偏序集及其定向完备化和Smyth幂的特征、浓度.得到了几个关系定理:1)连续偏序集的特征(浓度)等于其上Scott拓扑的特征(浓度),但小于等于其上Lawson拓扑的特征(浓度);2)连续偏序集的浓度大于或等于它的定向完备化的浓度,而特征小于或等于它的定向完备化的特征;3)连续domain的浓度大于或等于它的Smyth幂domain的浓度.
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| 关 键 词： | 连续偏序集 domain 定向完备化 Smyth幂domain 特征 浓度 |
| 文章编号： | 1007-6573（2006）01-0006-05 |
| 收稿时间： | 2005-09-12 |
| 修稿时间： | 2005-09-12 |
On Characters and Densities of Continuous Posets and Smyth Power Domains |
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| LIU Hai-yu,XU Luo-shan. On Characters and Densities of Continuous Posets and Smyth Power Domains[J]. Journal of Xuzhou Normal University(Natural Science Edition), 2006, 24(1): 6-10 |
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| Authors: | LIU Hai-yu XU Luo-shan |
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| Affiliation: | 1. Department of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu, 221116, China; 2. Department of Foundation Courses, Jiangsu Teachers College of Technology, Changzhou, Jiangsu, 213001, China ; 3. Department of Mathematics, Yangzhou University, Yangzhou, Jiangsu, 225002, China |
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| Abstract: | The concepts of characters and densities on continuo us domains are generalized to the setting of continuous posets.Relations of chara cters and densities among continuous posets,intrinsic topologies,directed compl etions and Smyth power domains are examined.The main results are: 1) the charac ter and density of a continuous poset are respectively equal to those of the rel ated space with Scott topology,but they are respectively less than or equal to those of the related space with the Lawson topology;2) the density of a contin uous poset is greater than or equal to that of its directed completion,while th e character is less than or equal to that of its directed completion; 3) the den sity of a continuous domain is greater than or equal to that of its Smyth power domain. |
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| Keywords: | continuous poset domain directed completion Smyth power domain character density |
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