LF拓扑空间中δT_(i)-分离性与加强的δT_(i)-分离性  

Several δT_(i)-Separability and Enhanced δT_(i)-Separability in LF Topological Space

作　　者：刘生云 王小霞[1] 王玉焕 Liu Shengyun;Wang Xiaoxia;Wang Yuhuan(Yan′an University,Yan′an 716000,China)

机构地区：[1]延安大学,陕西延安716000

出　　处：《廊坊师范学院学报（自然科学版）》2024年第2期5-10,共6页Journal of Langfang Normal University(Natural Science Edition)

基　　金：国家自然科学地区基金项目(12261090);陕西省自然科学基础研究计划项目(2018JM1042);延安大学研究生教育创新计划项目(YCX2024048)。

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δT_(i)-分离性和加强的δT_(i)-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δT_(i)-分离性与其底空间的δT_(i)-分离性的关系。With the in-depth study of different types of generalized open sets,the axiomof 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 tofurther enrich and improve the separability theory in LFtopological spaces,concepts such asδ-open sets andδ-far-field are utilized,Several specialδTi-separability and enhancedδTi-separability in LFtopological spaces are defined,and a series of properties such as L-good generalization,heritability,multiplicability,δ-weak homeo-morphisminvariance are proved.The relationship between theδTi-separability of weakly induced LF topological spaces and theδTi-separability of their base spaces is alsoexplained.

关 键 词：δ-开集 δ-远域 δT_(i)-分离性 强δT_(i)-分离性 

分 类 号：O189.1[理学—数学]