闭包空间的下半连续函数的表示  

Representations of Lower Semi-continuous Mappings of Closure Spaces

作　　者：路玲霞 赵蕾[1] 姚卫 LU Ling-xia;ZHAO Lei;YAO Wei(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《模糊系统与数学》2024年第3期28-33,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金项目(12231007,12371462)。

摘　　要：本文研究了从闭包空间X到完备格L的下半连续函数的两类形式的表示,证明了:(1)对于每个闭包空间(X,η),其到L的下半连续函数与从L到η的保交映射一一对应:(2)L是完全分配格当且仅当对于任意闭包空间(X,η),其下半连续函数与从η到L的保交映射一一对应;(3)闭包空间(X,η)是全连续的当且仅当对于每个完备格L,X的下半连续函数与从η到L的保交映射一一对应。This paper studies two kinds of representations of lower semi-continuous mappings from closure spaces to a complete lattice L.It is proved that:(1)for every closure space(X,η),its lower semi-continuous mappings are bijective to meet-preserving mappings from L to η;(2)a complete lattice L is completely distributive iff for every closure space(X,η),its lower semi-continuous mappings are bijective to meet-preserving mappings from η to L:(3)a closure space(X,η)is toally-continuous iff for every complete lattice L,the lower semi-continuous mappings of X are bijective to meet-preserving mappings from L to η.

关 键 词：闭包空间 下半连续函数 完全分配格 全连续空间 保交映射 

分 类 号：O159[理学—数学]