闭包算子与Topped交结构的序关系-陕西师范大学学报期刊社网站

陕西师范大学学报（自然科学版）

数学与计算机科学

闭包算子与Topped交结构的序关系

刘妮

(陕西师范大学数学与信息科学学院，陕西西安 710062)

刘妮,女,副教授,博士，主要从事格上拓扑学和拟阵理论的研究.E-mail:niliu@snnu.edu.cn.

摘要:

研究了同一集合上的几种闭包算子与相应的Topped（带有最大元的）交结构之间的序关系. 在任意集合X上的全体闭包算子之集C(X)、Topped交结构之集I(X)、代数闭包算子之集AC(X)、代数Topped交结构之集AI(X)上分别定义了偏序,证明了C(X)、AC(X)、I(X)及AI(X)都是完备格,并且C(X)与I(X)对偶同构,AC(X)与AI(X)对偶同构.得到了集合X上的全体拓扑闭包算子之集TC(X)与全体拓扑Topped交结构之集TI(X) 对偶同构,拟阵闭包算子之集MC(X)与拟阵Topped交结构之集MI(X)（拟阵闭集族）对偶同构.

关键词：

闭包算子; Topped交结构; 代数闭包算子; 完备格; 对偶同构

收稿日期：

2010-04-20

中图分类号：

O189.1

文献标识码：

文章编号：

1672-4291(2010)06-0014-04

基金项目：

国家自然科学基金资助项目(107181121)；陕西师范大学优秀科技预研项目(200702002).

Doi:

Order relations between closure operators and topped intersection structures

LIU Ni

(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)

Abstract:

The order relations between closure operators and topped intersection structures on the same set are discussed. Some partial orders on C(X) (the set of all closure operators on X)、I(X) (the set of all Topped intersection-structures on X)、AC(X)(the set of all algebraic closure operators on X) and AI(X)(the set of all algebraic closure operators on X) are introduced, respectively. These four sets are proved to be complete lattices.It is proved that C(X) is dually isomorphic to I(X), and AC(X) is dually isomorphic to AI(X). TC(X) (the set of all topological closure operators on X) is dually isomorphic to TI(X) (the set of all topological intersection structures on X), and MC(X) (the set of all matroid closure operators on X) is dually isomorphic to MI(X) (the set of all matroid intersection structures on X).

KeyWords:

closure operator; Topped intersection structure; algebraic closure operator; complete lattice; dual isomorphism