| 拟一致结构与拟邻近结构的相互确定 |
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| 引用本文： | 汪义瑞,赵虎.拟一致结构与拟邻近结构的相互确定[J].内蒙古师范大学学报(自然科学版),2011(4). |
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| 作者姓名： | 汪义瑞 赵虎 |
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| 作者单位： | 安康学院数学系;陕西师范大学数学与信息科学学院; |
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| 基金项目： | 国家自然科学基金资助项目(10271069); 安康学院科研项目(AYQDZR200912) |
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| 摘 要： | 证明了对每个给定的集合X,可以在QP(X)(X上拟邻近结构的全体)上赋予适当的序关系<,使得(QP(X),<)是与(TQU(X),<)同构的完备格,其中TQU(X)是X上全有界拟一致结构的全体.因此,可以用拟邻近结构确定集合X上的全有界拟一致结构.
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| 关 键 词： | 完备格 全有界拟一致结构 拟邻近结构 完备格同构 |
Reciprocally Determining of Quasi-uniformities and Quasi-proximities |
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| WANG Yi-rui,ZHAO Hu.Reciprocally Determining of Quasi-uniformities and Quasi-proximities[J].Journal of Inner Mongolia Normal University(Natural Science Edition),2011(4). |
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| Authors: | WANG Yi-rui ZHAO Hu |
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| Institution: | WANG Yi-rui1,ZHAO Hu2(1.Department of Mathematics,Ankang College,Ankang 725000,Shaanxi,China,2.College of Mathematics and Information Sciences,Shaanxi Normal University,Xi'an 710062,China) |
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| Abstract: | In this paper,it is proved that,for a given set X,an appropriate partial order < can be defined on QP(X)(the set of all Quasi-proximities on the set X),such that(QP(X),<) is a complete lattice which is isomorphic with(TQU(X),<)(the set of all totally bounded Quasi-uniformities on X).Thus a quasi-proximities on a set X can be determined by a totally bounded Quas-uniformity. |
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| Keywords: | complete lattice totally bounded quasi-uniformity quasi-proximities complete lattice isomorphism |
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