| 闭包算子格及其分配性 |
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| 引用本文： | 崔艳丽,吴洪博. 闭包算子格及其分配性[J]. 云南师范大学学报(自然科学版), 2009, 29(6): 14-17 |
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| 作者姓名： | 崔艳丽 吴洪博 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西,西安,710062 |
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| 基金项目： | 国家自然基金，陕西省师范大学重点科研基金 |
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| 摘 要： | 基于对闭包运算的性质研究,引入了闭包算子以及同一集合上的闭包算子之间的通常序关系概念,构造出同一集合上的闭包算子关于通常序的上下确界,使得同一集合上的所有闭包算子关于定义的算子间的通常序构成完备格（闭包算子格）.同时证明了闭包算子格不满足分配性。
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| 关 键 词： | 拓扑 闭包算子 完备格 闭包算子格 分配格 |
Closure Operator Lattice and it's Distributive Law |
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| CUI Yan-li,WU Hong-bo. Closure Operator Lattice and it's Distributive Law[J]. Journal of Yunnan Normal University (Natural Sciences Edition), 2009, 29(6): 14-17 |
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| Authors: | CUI Yan-li WU Hong-bo |
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| Affiliation: | (College of Mathematics ＆Information Science , Shaanxi Normal University, Xihn Shaanxi, 710062) |
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| Abstract: | Based on the research of closure operation＇s properties, closure operator and usual order between two closure operators on the given set have been introduced and least upper bound, greatest lower bound of closure operators on the given set have been constructed, thus all closure operators on the given set constitute a complete lattice with the usual order defined in this paper. Simultaneously it is proved that the closure operator lattice does not satisfy the distributive law. |
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| Keywords: | topology closure operator complete lattice closure operator lattice distributive lattice |
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