k-结构空间的性质及其应用  

Properties and applications of k-structured spaces

作　　者：黄书棋 王天浩 梁海兰 HUANG Shuqi;WANG Tianhao;LIANG Hailan(College of Mathematics and Statistics,Fuzhou University,Fuzhou,Fujian 350108,China)

机构地区：[1]福州大学数学与统计学院,福建福州350108

出　　处：《福州大学学报（自然科学版）》2023年第1期9-12,共4页Journal of Fuzhou University(Natural Science Edition)

基　　金：福建省自然科学基金资助项目(2019J05033);福建省中青年教师教育科研资助项目(JAT190022)。

摘　　要：定义并探讨k-结构空间范畴的概念和基础性质,证明完全正则拓扑空间范畴和仿射代数簇范畴均可视为k结构空间范畴的子范畴.同时,讨论k-结构子空间与k-结构商空间的构造,并证明这两种构造分别对应于k-结构空间范畴的等值子和余等值子.最后,刻画了k-结构空间的Zariski拓扑的不可约性,并给出子空间覆盖定理的一个新视角下的有趣证明.In this paper,we define and discuss the concept and basic properties of categories of k-structured spaces,and prove that the category of completely regular topological spaces and categories of affine algebraic varieties can be regarded as subcategories of some categories of k-structured spaces.Moreover,this paper also discusses the construction of k-structure subspace and k-structure quotient space,and proves that these two constructions correspond to the equalizer and co-equalizer of categories of k-structure spaces respectively.Finally,we characterize the irreducibility of Zariski topologies in k-structured spaces,and give an interesting proof of the subspace covering theorem from a new view.

关 键 词：k-结构空间 k-态射 Zariski拓扑 子空间覆盖定理 

分 类 号：O143[理学—数学]