| 半连续格上的半基和局部半基 |
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| 引用本文： | 李高林,徐罗山,陈昱.半连续格上的半基和局部半基[J].模糊系统与数学,2010,24(1). |
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| 作者姓名： | 李高林 徐罗山 陈昱 |
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| 作者单位： | 1. 盐城师范学院,数学科学学院,江苏,盐城,224002;扬州大学,数学科学学院,江苏,扬州,225002
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;60774073);;江苏省高校自然科学基础研究项目(08KJD110008);;盐城师范学院科研项目(07YCKL070) |
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| 摘 要： | 在完备格上引入了半基和局部半基的概念,给出了半基和局部半基的性质及若干等价刻画,证明了一个完备格是半连续格当且仅当它具有半基也当且仅当它每点有局部半基。在此基础上定义了半连续格的权和特征,探讨了半连续格的权和特征与其上赋予半Scott拓扑和半Lawson拓扑时的拓扑空间的权和特征的关系。解决了文献8](赵彬,刘妮.连续Domain的特征和浓度,陕西师范大学学报,2002,30(2):1~6)中提出的一个问题。
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| 关 键 词： | 半连续格 半基 局部半基 权 特征 |
Semi-bases and Local semi-bases on Semicontinuous Lattices |
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| LI Gao-lin,XU Luo-shan,CHEN Yu.Semi-bases and Local semi-bases on Semicontinuous Lattices[J].Fuzzy Systems and Mathematics,2010,24(1). |
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| Authors: | LI Gao-lin XU Luo-shan CHEN Yu |
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| Institution: | 1.School of Mathematics Science/a>;Yancheng Teachers College/a>;Yancheng 224002/a>;China/a>;2.School of Mathematics Science/a>;Yangzhou University/a>;Yangzhou 225002/a>;China |
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| Abstract: | In this paper,the concepts of semi-bases and local semi-bases on semicontinuous lattices are introduced.Some properties and equivalent characterizations of semi-bases and local semi-bases are obtained.It is proved that a complete lattice is semicontinuous if and only if it has semi-bases if and only if it has local semi-bases for all points.The concepts of weights and characters on semicontinuous lattices are also introduced.Relations between the weights(resp.,characters) of a semicontinuous lattice and tha... |
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| Keywords: | Semicontinuous Lattice Semi-base Local Semi-base Weight Character |
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