拟代数空间的若干性质  

Several properties of quasialgebraic spaces

作　　者：王武[1] WANG Wu(Zhonghuan Information College,Tianjin University of Technology,Tianjin 300380,China)

机构地区：[1]天津理工大学中环信息学院,天津300380

出　　处：《高师理科学刊》2025年第2期5-9,共5页Journal of Science of Teachers'College and University

基　　金：天津市教委科研计划项目(2023KJ281)。

摘　　要：利用拟连续闭包算子和紧元研究了拟代数空间的拟代数性,证明了拟代数空间在拟连续闭包算子下的不变性,同时给出了拟连续代数空间在一定条件下的一些等价刻画.主要结论为:(1)拟代数空间的拟连续闭包算子象是拟代数空间;(2)在一定条件下,定向空间X是拟代数空间当且仅当:对于任意a,b∈X,a≠b蕴含fin_(k)(a)≠fin_(k)(b).The quasicontinuous closure operators and compact elements are used to study the quasialgebraic properties of quasialgebraic spaces,the invariance of quasialgebraic spaces is proven under quasicontinuous closure operators,and some equivalent characterizations of quasicontinuous algebraic spaces under certain conditions are given.The main conclusions are as follows:(1)The quascontinuous closure operator image of quasialgebraic spaces are quasialgebraic spaces;(2)Under certain conditions,a directed space X is quasialgebraic space if and only if a≠b implies fin_(k)(a)≠fin_(k)(b) for any a,b∈X.

关 键 词：定向空间 拟代数空间 拟连续闭包算子 拟代数逼近元 

分 类 号：O153.1[理学—数学]