稳定连续半格的闭包空间表示  

A representation of stably continuous semilattices by closure spaces

作　　者：王胜文 张冰 马俊叶 王龙春[2] WANG Shengwen;ZHANG Bing;MA Junye;WANG Longchun(School of Mathematics and Statistics,Liupanshui Normal University,553004,Liupanshui,Guizhou;School of Mathematical Sciences,Qufu Normal University,273165,Qufu,Shandong;School of Applied Science,Taiyuan University of Science and Technology,030024,Taiyuan,Shanxi,PRC)

机构地区：[1]六盘水师范学院数学与统计学院,贵州省六盘水市553004 [2]曲阜师范大学数学科学学院,山东省曲阜市273165 [3]太原科技大学应用科学学院,山西省太原市030024

出　　处：《曲阜师范大学学报（自然科学版）》2024年第1期61-66,共6页Journal of Qufu Normal University(Natural Science)

基　　金：曲阜师范大学校级教改项目(22jg30);曲阜师范大学大学生创新训练项目(XJ20210065);六盘水师范学院重点学科建设项目—数学重点培育学科(LPSSYZDPYXK201709);山西省基础研究计划项目(202103021223272);太原科技大学博士科研启动基金(20202049)。

摘　　要：为稳定连续半格构建合适的闭包空间表示,引入了可乘闭包空间的概念,证明了可乘闭包空间的正则闭集族在集合包含关系下构成了一个稳定连续半格,并且所有的稳定连续半格都可在序同构的意义下由此生成.进一步提出了可乘闭包空间之间逼近映射的概念,刻画了以Scott连续映射为态射的稳定连续半格范畴和以逼近映射为态射的可乘闭包空间范畴间的等价性.The main purpose of this paper is to establish an appropriate representation for stably continuous semilattices by closure spaces.The notion of a multiplicative closure space is introduced.It is shown that the collection of all regular closed sets of multiplicative closure space under set inclusion forms a stably continuous semilattice and every stably continuous semilattice can be obtained in this way up to isomorphism.Moreover,the notion of an approximable mapping between multiplicative closure spaces is presented to characterize the equivalence between the category of stably continuous semilattices with Scott continuous functions and that of multiplicative closure spaces with approximable mappings.

关 键 词：闭包空间 DOMAIN理论 稳定连续半格 Scott连续映射 范畴等价 

分 类 号：O153.1[理学—数学]