公理化凸空间的闭包算子和内部算子  

Closure Operators and Interior Operators of Axiomatic Convex Spaces

作　　者：王冰 

机构地区：[1]牡丹江师范学院数学科学学院,黑龙江牡丹江157011

出　　处：《数学的实践与认识》2017年第17期247-252,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金面上项目(11371002);牡丹江师范学院国家级课题培育项目(科技)(GP2017001);牡丹江师范学院博士科研启动基金项目(MNUB201511);牡丹江师范学院教育教学改革项目(16-JG18036)

摘　　要：引入公理化凸空间框架下的闭包算子和内部算子,分别称之为凸闭包算子和凸内部算子.结果表明,论域X上的凸结构全体不仅等价于论域X上的凸闭包算子全体,而且等价于论域X上的凸内部算子全体.In this paper, the concepts of closure operators and interior operators in the framework of axiomatic convex spaces are introduced, which are called convex closure operators and convex interior operators, respectively. It is shown that the family of convex structures on X is not only equivalent to the family of convex closure structures on X, but also equivalent to the family of convex interior structures on X.

关 键 词：公理化凸空间 凸闭包算子 凸内部算子 

分 类 号：O189.13[理学—数学]