预导算子、预差导算子及预拓扑

预导算子、预差导算子及预拓扑

杨小飞, 李生刚*

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 杨小飞

Pre-derived operators, pre-difference derived operators and pre-topologies

YANG Xiao-fei, LI Sheng-gang*

College of Mathematics and Information Sciences, Shaanxi Normal University,Xi'an 710062, Shanxi, China

Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: YANG Xiao-fei

摘要/Abstract

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。

关键词: 预导算子, 完备格 , 预拓扑, 差导算子, 预差导算子, 导算子

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).

Key words: complete lattice , pre-topology, difference derived operater, pre-difference derived operater, derived operater, pre-derived operater

中图分类号:

O189.1

杨小飞,李生刚* . 预导算子、预差导算子及预拓扑[J]. J4, 2007, 42(12): 55-57 .

YANG Xiao-fei,LI Sheng-gang* . Pre-derived operators, pre-difference derived operators and pre-topologies[J]. J4, 2007, 42(12): 55-57 .

参考文献

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