| 连续偏序集及其Smyth幂的几个等权定理 |
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| 引用本文： | 刘海玉,徐罗山.连续偏序集及其Smyth幂的几个等权定理[J].模糊系统与数学,2006,20(2):44-49. |
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| 作者姓名： | 刘海玉 徐罗山 |
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| 作者单位： | 1. 江苏技术师范学院,基础部,江苏,常州,213015
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)，江苏省教育厅基金资助项目(FK0310060) |
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| 摘 要： | 推广连续D om a in的权的概念到连续偏序集上,探讨连续偏序集的权、相应内蕴拓扑的权、定向完备化的权以及Sm yth幂D om a in的权间的关系。得到了几个等权定理:(1)连续偏序集的权与其上Scott拓扑、L aw son拓扑的权相等;(2)连续偏序集的权与其定向完备化的权相等;(3)无穷连续D om a in的权与其Sm yth幂D om a in的权相等;(4)有限D om a in的权小于或等于它的Sm yth幂D om a in的权。
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| 关 键 词： | 连续偏序集 Domain 定向完备化 Smyth幂Domain 权 |
| 文章编号： | 1001-7402（2006）02-0044-06 |
| 收稿时间： | 2005-03-15 |
| 修稿时间： | 2005年3月15日 |
Some Theorems on the Weights of Continuous Posets and Smyth Power Domains |
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| LIU Hai-Yu,XU Luo-Shan.Some Theorems on the Weights of Continuous Posets and Smyth Power Domains[J].Fuzzy Systems and Mathematics,2006,20(2):44-49. |
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| Authors: | LIU Hai-Yu XU Luo-Shan |
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| Institution: | 1. Department of Basic Course,Jiangsu Teachers College of Technology,Changzhou 213015,China; 2. Department of Mathematics,Yangzhou University,Yangzhou 225002,China |
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| Abstract: | The concept of weights on continuous domains is generalised to the setting of continuous(posets.) Relations of the weights of a continuous poset,the directed completion of the poset and some intrinsic topologyies on the poset are examined.The main theorems are:(1) The weight of a(continuous) poset is equal to the weight of the Scott topology and is also equal to the weight of the(Lawson) topology(of the poset).(2) The weight of a continuous poset is equal to the weight of the(directed) completion of the poset.(3) The weight of an infinite continuous domain is equal to the(weight) of its Smyth power domain.(4) The weight of a finite domain is less than or equal to that of its Smyth power domain. |
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| Keywords: | Continuous Poset Domain Directed Completion Smyth Power Domain Weight |
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