关于M-结构新的分离性及弱M-连续映射的研究
发布时间：2018-09-09 18:29
【摘要】：广义拓扑是一般拓扑的推广,具有一般拓扑中的一些好的性质,同时它也极大地丰富和发展了一般拓扑的研究.1997年,匈牙利数学家A.Csaszar首先定义了广义拓扑,并且研究了广义拓扑性质以及广义连续,得到了很多有意义的结果.2012年,A.Al-Omari和T.Noiri定义了M 结构.同年,M.Navaneetha-krishnan 和 S.Thamaraiselvi 进一步研究了M-结构的一些性质.2015年,李中元研究了 M-结构中的分离性和(M1,M2)-连续映射的性质,得到了M 结构中很多有用的结论.本文是在前面学者研究的基础上进一步研究了M-结构中新的分离性以及弱M-连续映射.第一章,我们介绍M-结构产生的具体背景、研究和发展的概况,同时介绍了论文中要用到的主要定义、定理以及相关的记号.第二章,我们在M-空间中定义了g -闭集、M-内核、M-T1/2空间、并且讨论了相关的一些性质,同时也在M-R0和M-R1空间中进一步研究了这些分离性的新的一些性质和关系.第三章,我们给出了弱M-连续映射和弱M-闭包连续映射定义,并研究了弱M-连续映射的性质以及弱M-连续映射和弱M-闭包连续映射的关系.
[Abstract]:Generalized topology is a generalization of general topology. It has some good properties in general topology. At the same time, it greatly enriches and develops the study of general topology. In 1997, Hungarian mathematician A. Csaszar first defined generalized topology, and studied the properties of generalized topology and generalized continuity, and obtained many meaningful results. In the same year, M. Navaneetha-krishnan and S. Thamaraiselvi further studied some properties of M-structures. In 2015, Li Zhongyuan studied the separability of M-structures and the properties of (M1, M2) -continuous mappings, and obtained many useful conclusions in M-structures. In the first chapter, we introduce the background of M-structure, the general situation of research and development, and the main definitions, theorems and related notations used in this paper. In the second chapter, we define g-closed sets, M-kernel, M-T1/2 spaces in M-spaces, and discuss them. In chapter 3, we give the definitions of weak M-continuous mappings and weak M-closure continuous mappings, and study the properties of weak M-continuous mappings and the relations between weak M-continuous mappings and weak M-closure continuous mappings.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O189.11
本文编号：2233219
[Abstract]:Generalized topology is a generalization of general topology. It has some good properties in general topology. At the same time, it greatly enriches and develops the study of general topology. In 1997, Hungarian mathematician A. Csaszar first defined generalized topology, and studied the properties of generalized topology and generalized continuity, and obtained many meaningful results. In the same year, M. Navaneetha-krishnan and S. Thamaraiselvi further studied some properties of M-structures. In 2015, Li Zhongyuan studied the separability of M-structures and the properties of (M1, M2) -continuous mappings, and obtained many useful conclusions in M-structures. In the first chapter, we introduce the background of M-structure, the general situation of research and development, and the main definitions, theorems and related notations used in this paper. In the second chapter, we define g-closed sets, M-kernel, M-T1/2 spaces in M-spaces, and discuss them. In chapter 3, we give the definitions of weak M-continuous mappings and weak M-closure continuous mappings, and study the properties of weak M-continuous mappings and the relations between weak M-continuous mappings and weak M-closure continuous mappings.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O189.11
【参考文献】
相关期刊论文 前1条
1 ;μ-Separations in generalized topological spaces[J];Applied Mathematics:A Journal of Chinese Universities(Series B);2010年02期
相关硕士学位论文 前1条
1 李中元;关于M-结构分离性及（M_1，M_2）-连续映射的研究[D];南京师范大学;2016年
，本文编号：2233219
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