稳定连续半格的闭包空间表示
A representation of stably continuous semilattices by closure spaces
王胜文 1张冰 2马俊叶 3王龙春2
作者信息
- 1. 六盘水师范学院数学与统计学院,553004,贵州省六盘水市
- 2. 曲阜师范大学数学科学学院,273165,山东省曲阜市
- 3. 太原科技大学应用科学学院,030024,山西省太原市
- 折叠
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.
Abstract
The main purpose of this paper is to establish an appropriate representation for stably contin-uous 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 stab-ly continuous semilattice and every stably continuous semilattice can be obtained in this way up to isomor-phism.Moreover,the notion of an approximable mapping between multiplicative closure spaces is presen-ted to characterize the equivalence between the category of stably continuous semilattices with Scott con-tinuous 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Key words
closure spaces/Domain theory/stably continuous semilattices/Scott continuous functions/categorical equivalence引用本文复制引用
基金项目
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)
出版年
2024
国家科技期刊平台
NSTL
维普
万方数据