算术半格的闭包空间表示  

A Representation of Arithmetic Semilattices by Closure Spaces

作　　者：张清霞 李庆国[1] 王龙春 ZHANG Qing-xia;LI Qing-guo;WANG Long-chun(School of Mathematics,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学数学学院,湖南长沙410082

出　　处：《模糊系统与数学》2021年第2期1-9,共9页Fuzzy Systems and Mathematics

摘　　要：本文主要讨论算术半格的闭包空间表示。首先通过在给定的闭包空间中增加适当的条件,提出了算术闭包空间的概念,并且给出了算术半格的闭包空间表示。接着提出了算术闭包空间之间的算术逼近映射的概念,并证明了以算术逼近映射作为态射的算术闭包空间范畴和以Scott连续函数作为态射的算术半格范畴之间的范畴等价性。This paper is mainly devoted to the representation of arithmetic semilattices by closure spaces. First, we propose the notion of arithmetic closure spaces by incorporating an additional structure into a given closure space and give the representation of arithmetic semilattices. Then, the notion of arithmetic approximable mappings between arithemetic closure spaces is proposed and we prove that the category of arithmetic closure spaces with arithmetic approximable mappings is equivalent to that of arithmetic semilattices with Scott continuous as morphism.

关 键 词：算术半格 算术闭包空间 范畴等价 

分 类 号：O159[理学—数学]