关于相对拓扑若干性质的研究

发布时间：2018-05-11 13:46

本文选题：相对拓扑 + L-预拓扑空间　；参考：《淮北师范大学》2016年硕士论文

【摘要】：摘要：在一般拓扑及相对拓扑性质的研究背景下,从相对乃空间、相对乃空间、相对正则空间和相对正规空间等方面对AV Arhangel skii所提出的相对拓扑性质进行了研究,并且得到了相对正规空间X的任一子集Y在X中都相对正规等结论,同时给出了相对拓扑的次正则性.在既约元的基础上定义了弱交既约元,同时将L-拓扑空间推广到L-预拓扑空间.在L-拓扑空间分离性的基础上,引入了L-预拓扑空间的次乃(i=1,2,3,4)的分离性.得到了若L-预拓扑空间所诱导的拓扑系统(copr(Lx),δ,1=)是次T的,则L-预拓扑空间也是次T的等系列结果.本文的主要内容如下：第一部分：给出了相对拓扑和L-拓扑空间以及格论和拓扑系统中的基本概念.第二部分：引入了L-预拓扑空间的次分离性,给出了它们之间的相互关系.同时给出了L — Fuzzy拓扑内部空间的相对分离性和次相对分离性,并且给出了它们之间的等价刻画,以及给出了相对乃分离性具有遗传性.第三部分：基于子拓扑系统的定义进一步研究了它的一些相关性质,同时研究了子拓扑系统的相对分离性和相对紧性,给出了子拓扑系统E相对于拓扑系统D为乃(i=1,2,21/2,3,4)的定义.并且证明了子拓扑系统E相对于D为正(i=1,2,3,4)的充要条件为Spat(E)相对于Spat(D)是乃的,子拓扑系统E相对于D为紧的充要条件为Spat(E)相对于Spat(D)是紧的.
[Abstract]:Abstract: under the background of general topology and relative topological properties, the relative topological properties proposed by AV Arhangel skii are studied from the aspects of relative normal space, relative regular space and relative normal space. In addition, we obtain the conclusion that any subset Y of relative normal space X is relatively normal in X, and give the subregularity of relative topology. Based on the irreducible element, the weakly intersecting irreducible element is defined, and the L-topological space is extended to the L-pretopological space. Based on the separation of L- topological spaces, the separability of L- pretopological spaces is introduced. If the topological system induced by the L- pretopological space is subT, then the L- pretopological space is also a subT series of results. The main contents of this paper are as follows: in the first part, the basic concepts of relative topology and L-topological space, lattice theory and topological system are given. In the second part, the subseparability of L-pretopological space is introduced, and the relationship between them is given. At the same time, the relative separation and subrelative separation of the inner space of L Fuzzy topology are given, and the equivalent characterizations between them are given, and it is also given that the relative separation is hereditary. Part three: based on the definition of subtopological system, some related properties are further studied, and the relative separation and relative compactness of subtopological system are studied, and the definition of subtopological system E relative to topological system D is given. It is proved that the subtopological system E is positive to D if and only if Spatt E is relative to Spatt D4, and that the subtopological system E is compact relative to D if and only if the subtopological system E is compact relative to Spatt D.
【学位授予单位】：淮北师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O189

【相似文献】