LF拓扑空间中δTi-分离性与加强的δTi-分离性
Several δTi-Separability and Enhanced δTi-Separability in LF Topological Space
刘生云 1王小霞 1王玉焕1
作者信息
摘要
随着不同类型推广型开集的深入研究,分离性公理也在不断发展.虽然关于LF拓扑空间中分离性的研究已经取得不少成果,但从不同层次结构的开集、闭集、远域等概念入手会得到不同的结果.为进一步丰富和完善LF拓扑空间中的分离性理论,利用δ-开集和δ-远域等概念,定义了 LF拓扑空间中几种特殊的δTi-分离性和加强的δTi-分离性,证明了这几种分离性的一系列性质,如L-好的推广、遗传性、可乘性、δ-弱同胚不变性等,并说明了弱诱导LF拓扑空间的δTi-分离性与其底空间的δTi-分离性的关系.
Abstract
With the in-depth study of different types of generalized open sets,the axiom of separability is also constantly developing.Although many achievements have been made in the study of separability in LFtopological spaces,different re-sults can be obtained by starting with concepts such as open sets,closed sets,and far-field with different hierarchical struc-tures.Therefore,in order to further enrich and improve the separability theory in LFtopological spaces,concepts such as 8-open sets and δ-far-field are utilized,Several special δTi-separability and enhanced δTi-separability in LFtopological spaces are defined,and a series of properties such as L-good generalization,heritability,multiplicability,δ-weak homeo-morphism invariance are proved.The relationship between the δTi-separability of weakly induced LF topological spaces and the δTi-separability of their base spaces is also explained.
关键词
δ-开集/δ-远域/δTi-分离性/强δTi-分离性Key words
δ-open set/δ-far field/δTi-separability/δTi-strong separability引用本文复制引用
出版年
2024
NETL
NSTL
万方数据