| 用弱内导算子确定闭包系统 |
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| 引用本文： | 高小燕.用弱内导算子确定闭包系统[J].纺织高校基础科学学报,2011,24(3):338-341. |
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| 作者姓名： | 高小燕 |
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| 作者单位： | 榆林学院数学与应用数学系,陕西榆林,719000 |
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| 基金项目： | 陕西省教育厅科技计划项目 |
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| 摘 要： | 引入了弱内导算子概念,证明了对于每个给定的集合X,可以给WE(X)(即X上的弱内导算子的全体)上赋予适当的序关系≤使得(WE(X),≤)与(CS(X),(∪))完备格同构.这里CS(X)是X上的闭包系统的全体.从而它们之间也是范畴同构的,因此可以用弱内导算子完全确定闭包系统最后讨论了弱内导算子的范畴性质.
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| 关 键 词： | 弱内导算子 闭包系统 完备格同构 余反射子范畴 |
Determination a closure system by a weak interior derived operator |
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| GAO Xiao-yan.Determination a closure system by a weak interior derived operator[J].Basic Sciences Journal of Textile Universities,2011,24(3):338-341. |
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| Authors: | GAO Xiao-yan |
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| Affiliation: | GAO Xiao-yan (Department of Mathematics and Applied Mathematics,Yulin College,Yulin,Shaanxi 719000,China) |
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| Abstract: | The notion of weak interior derived operator is introduced in this paper.It is proved that,for a given set X,an order relation ≤ can be defined on WE(X)(the set of all weak interior derived operators on X) such that(WE(X),≤) is a complete lattice which is isomorphic to(CS(X),■)(the set of all closure systems on X).An isomorphism also can be established between corresponding categories. Therefore,any closure system can be determined by a weak interior derived operator.Finally the properties of category of weak interior derived spaces are studied. |
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| Keywords: | weak interior derived operator closure system complete lattice isomorphism coreflective subcategory |
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