| 闭格的性质 |
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| 引用本文： | 李庆国,吴琼,伍秀华. 闭格的性质[J]. 湖南大学学报(自然科学版), 2014, 41(7): 113-116 |
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| 作者姓名： | 李庆国 吴琼 伍秀华 |
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| 作者单位： | （1.湖南大学 数学与计量经济学院,湖南 长沙410082;2.中南林业大学 理学院,湖南 长沙410082） |
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| 基金项目： | 国家自然科学基金资助项目(11071061);湖南省科技计划项目(2012FJ3145)资助 |
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| 摘 要： | 对闭格进行研究,给出了闭格的等价刻画,讨论了闭格与Locale的关系,并证明了闭格的笛卡尔乘积仍是闭格.同时,得到了闭格在保任意并的满态射下仍是闭格,最后证明了闭格在闭包运算下的像是闭格.
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| 关 键 词： | 闭格 并不可约元 Locale 笛卡尔乘积 闭包运算 |
Some Properties of the Closed Lattices |
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| LI Qing-guo,WU Qiong,WU Xiu-hua. Some Properties of the Closed Lattices[J]. Journal of Hunan University(Naturnal Science), 2014, 41(7): 113-116 |
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| Authors: | LI Qing-guo WU Qiong WU Xiu-hua |
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| Affiliation: | (1.College of Mathematics and Econometrics, Hunan Univ , Changsha, Hunan410082, China;2.School of Sciences, Central South Univ of Forestry and Technology, Changsha, Hunan410082, China) |
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| Abstract: | In this paper, we investigated some properties of the closed lattices and gave their characterizations. The relationship between the Locale and the closed lattice was investigated. It is proved that the Cartesian product of the close lattice is still closed lattice. Moreover, we obtained the result that the closed lattice under a surjective map preserving arbitrary sups is still the closed lattice. Finally, we studied the property of the image of the closed lattice under the closure operator. |
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| Keywords: | closed lattice join-irreducible element Locale Cartesian product closure operation |
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