摘要
基于子基的覆盖拓扑空间主要将覆盖所成子基引入粗糙集框架来诱导变异拓扑,已经具有连通性、分离性、可数性与紧致性的性质研究,但尚未涉及序列紧致性讨论.本文主要探讨基于子基的覆盖拓扑空间的序列紧致性.针对基于子基的覆盖拓扑空间,在深化紧致性的基础上,定义了序列紧致性,并研究了相关性质,最后提供一个说明实例.所得结果对基于子基的覆盖拓扑空间进行了系统完善与深入刻画.
The covering topological space based on a subbase mainly introduces a covering(which constitutes a usual topological subbase) into the rough set framework to induce a variant topological space.At present,its topological properties concern only the connectedness,separability,countability and compactness.Thus,its sequence compactness is not previously studied but will be explored in this paper.Aiming at the covering topological space based on a subbase,the compactness is first deepened,the sequence compactness is then defined to achieve relevant properties,and an illustration example is finally provided.The obtained results systematically complete and deeply describe the covering topological space based on a subbase.
作者
黄宜纯
冯树凯
张贤勇
HUANG Yi-chun;FENG Shu-kai;ZHANG Xian-yong(School of Computer Science,Sichuan Technology and Business University,Chengdu 611745,China;School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,China)
出处
《数学的实践与认识》
北大核心
2020年第4期191-196,共6页
Mathematics in Practice and Theory
基金
国家自然科学基金(61673285)
四川省科技基金(19YYJC2845)
四川省青年基金(2017JQ0046)
四川省教育厅科研项目(18ZA0410)
四川工商学院转型发展重点项目(2017SFTD6).
关键词
覆盖拓扑空间
子基
序列紧致性
紧致性
covering topological space
subbase
sequence compactness
compactness
