闭包系统的确定

J4 ›› 2009, Vol. 44 ›› Issue (6): 18-21.

闭包系统的确定

鲜路，李生刚*,严小平

陕西师范大学数学与信息科学学院，陕西西安 710062

收稿日期:2008-08-07 发布日期:2011-06-03
通讯作者: 李生刚(1959-)，男，教授，博士生导师，主要研究方向格上拓扑学与拟阵. Email: she nggangli@yahoo.com.cn
作者简介:鲜路(1985-)，男，硕士研究生，主要从事格上拓扑学与模糊聚类分析领域的研究
基金资助:
国家自然科学基金资助项目(10271069)；陕西师范大学研究生培养创新基金资助项目(2009CXS029)

Determination of closure systems

XIAN Lu, LI Shenggang*, YAN Xiaoping

College of Mathematics and Information Science, Shaanxi Normal University, Xi’ an 710062, Shaanxi, China

Received:2008-08-07 Published:2011-06-03

摘要/Abstract

摘要：

证明了可以在WCL(X)(X上的弱闭包算子的全体)、 WIN(X)(X上的弱内部算子的全体)、 WOU (X) (X上的弱外部算子的全体)、 WB (X) (X上的弱边界算子的全体)、WD( X)(X上的弱导算子的全体)、 WD* (X)(X上的弱差导算子的全体)、 WR( X)(X上的弱远域系算子的全体)和WN(X)(X上的弱邻域系算子的全体)上定义适当的序关系,使它们成为与(CS(X),〖JX-*5][JX*5])同构的完备格(其中CS(X)是给定集合X上的闭包系统的全体)。

关键词: 闭包系统;弱内部算子;弱外部算子;弱边界算子;弱差导算子; 弱远域系算子

Abstract:

For an abitrary set X, appropriate order relations on WCL(X) (the set of all weak closure operators), WIN(X) (the set of all weak interior operators), WOU(X) (the set of all weak exterior operators), WB(X) (the set of all weak boundary operators), WD(X) (the set of all weak derived operators), WD*(X) (the set of all weak difference derived operators), WR(X) (the set of all weak remote neighborhood system operators) and WN(X) (the set of all weak neighborhood system operators) can be defined respectively, which make WCL(X), WIN(X), WOU(X), WB(X), WD(X), WD*(X), WR(X) and WN(X) to be complete lattices that are ismorphic to (CS(X),CS(X) is the set of all closure systems on X.

Key words: closure system; weak interior operator; weak exterior operator; weak boundary operator; weak difference derived operator; weak remote neighborhood s ystem operator

中图分类号:

O1891

. 闭包系统的确定[J]. J4, 2009, 44(6): 18-21.

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