安徽大学学报（自然科学版）2025，Vol.49Issue(5)：11-18,8.DOI:10.3969/j.issn.1000-2162.2025.05.002
拟连续domain上的广义理想收敛
Generalized ideal convergence on quasi-continuous domains
摘要
Abstract
In this paper,the concepts of generalized ideal inf-limit and generalized ideal final lower bound limit are introduced in the directed complete poset,and their relations with Scott topology and Lawson topology are studied.The main results are as follows:(1)On directed complete posets,generalized ideal inf-limit topology is consistent with Scott topology;(2)Generalized ideal inf-limitis convergence is topological if and only if directed complete posets are quasi-continuous domains;(3)In quasi-continuous domain,generalized ideal final lower bound limit topology is consistent with Lawson topology,and a sufficient condition of continuous domain is given.关键词
拟连续domain/广义理想下极限/广义理想终下界极限/Scott拓扑/Lawson拓扑Key words
quasi-continuous domain/generalized ideal inf-limit/generalized ideal final lower bound limit/Scott topology/Lawson topology分类
数理科学引用本文复制引用
王武,谭彬,张舜..拟连续domain上的广义理想收敛[J].安徽大学学报（自然科学版）,2025,49(5):11-18,8.基金项目
国家自然科学基金青年基金资助项目(11401435) （11401435）
天津市教委科研计划项目(2023KJ281) （2023KJ281）
2021年高等学校大学数学教学研究与发展中心教学改革项目(CMC20210115) （CMC20210115）
