| 预导算子、预差导算子及预拓扑 |
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| 引用本文： | 杨小飞,李生刚.预导算子、预差导算子及预拓扑[J].山东大学学报(理学版),2007,42(12):55-57. |
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| 作者姓名： | 杨小飞 李生刚 |
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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： | 国家自然科学基金;陕西师范大学校科研和教改项目 |
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| 摘 要： | 引入了预导算子和预差导算子的概念,证明了对每个给定的集合X,可以给PD(X)(即X上预导算子的全体)和PDD(X)(即X上预差导算子的全体)上赋予适当的序≤使得(PD(X),≤)和(PDD(X),≤)是与(PT(X),)同构的完备格,这里PT(X)是X上预拓扑的全体。
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| 关 键 词： | 预导算子 导算子 预差导算子 差导算子 预拓扑 完备格 |
| 文章编号： | 1671-9352（2007）12-0055-03 |
| 收稿时间： | 2007-07-23 |
| 修稿时间： | 2007年7月23日 |
Pre-derived operators, pre-difference derived operators and pre-topologies |
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| YANG Xiao-fei,LI Sheng-gang.Pre-derived operators, pre-difference derived operators and pre-topologies[J].Journal of Shandong University,2007,42(12):55-57. |
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| Authors: | YANG Xiao-fei LI Sheng-gang |
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| Institution: | College of Mathematics and Information Sciences, Shaanxi Normal University,Xi'an 710062, Shanxi, China |
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| Abstract: | The concepts of pre-derived operator and pre-difference derived operator were introduced. It was proved that, for a given set X, appropriate order relations≤can be defined on PD(X) (the set of all pre-derived operators on X) and PDD(X) (the set of all pre-difference derived operators on X), respectively, such that both (PD(X), ≤) and (PDD(X), ≤) are complete lattices which are isomorphic to (PT(X))(the set of all pre-topologies on the set X). |
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| Keywords: | pre-derived operater derived operater pre-difference derived operater difference derived opemter pre-topology complete lattice |
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