局部紧正则Locale的紧正则反射  

The Compact Regular Reflection of Locally Compact Regular Locale

作　　者：李雨珈 孙向荣[1] LI Yujia;SUN Xiangrong(School of Science,Nanjing University of Posts and Telecommunications,Nanjing Jiangsu 210023,China)

机构地区：[1]南京邮电大学理学院,江苏南京210023

出　　处：《江西师范大学学报（自然科学版）》2019年第1期28-30,共3页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(10926104)资助项目

摘　　要：关于如何给出locale的紧正则反射构造一直是locale理论中最重要研究课题,通过给出补紧元的定义,进而给出局部紧正则locale的紧正则反射的一个构造性描述,并保证了局部紧正则定义在locale上和在拓扑空间上的一致性.同时证明了若A是局部紧locale,则CR(A)(由A的所有理想组成的理想格Idl(A)的子frame)是紧正则locale;并对于局部紧正则locale A,CR(A)是A的紧正则反射,并给出了具体的反射关系图.About how to give a construction of the compact regular reflection for locales is the most important issue in Locale theory. By given the definition of the co-compact element,a constructive description of the compact regular reflection for locally compact regular locales will be described,it also ensures that the definition of locally compact regular in the locale and in the topological space is consistent. At the same time,it is proved that if the local A is locally compact,then CR( A)( the sub-frame of the ideal lattice composed of all ideals) is the compact regular locale,and for the locally compact regular A,CR( A) is the compact regular reflections of locale A,the specific reflection relationship is also given.

关 键 词：局部紧正则locale 紧正则反射 局部紧locale 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]