关于σ-结构中σ-连续映射及分离性研究

发布时间：2018-07-09 11:43

本文选题：σ-结构 + σ-开集　；参考：《南京师范大学》2017年硕士论文

【摘要】：2013年,Y. K. Kim和W. K. Min在广义拓扑的基础上定义了 σ-结构,σ-开集,并在此基础上讨论了σ-结构的一些性质和拟扩充运算,而且得到了一些有趣的结果.本文在上述研究的基础上进一步给出了σ-连续映射,(σ_1,σ_2) 连续映射定义以及σ-分离性,D_σ-分离性的定义,并且研究了它们的相关性质.具体来说,在第一章里,我们介绍了 σ-结构产生的背景,研究发展概况,同时介绍了论文中所用到的主要定义定理和相关的符号.在第二章里,我们首先给出了 σ-结构,σ-开集的定义,讨论了σ-开集的性质,用σ-开集定义了 σ-连续映射,(σ_1,σ_2)-连续映射,并且研究了它们的相关性质.在第三章里,我们在σ-空间的基础上定义了σ-T_0空间,σ-T_1空间,σ-T_2空间,σ-T_3空间,σ-T_4空间以及σ-D_0空间,σ-D_1空间,σ-D_2空间,σ-R_0空间,σ-R_1空间,并且进一步研究了他们的性质.
[Abstract]:In 2013, Y. K. Kim and W. KMin defined 蟽 -structure, 蟽 -open set on the basis of generalized topology. On this basis, some properties and quasi-extended operations of 蟽 -structure were discussed, and some interesting results were obtained. In this paper, the definitions of 蟽 -continuous mappings, (蟽 _ S _ 1, 蟽 _ S _ 2) continuous mappings and 蟽 -separability D _ 蟽 -separability are further given, and their related properties are studied. Specifically, in Chapter 1, we introduce the background of 蟽 -structure, research and development, and introduce the main definition theorems and related symbols used in this paper. In chapter 2, we first give the definition of 蟽 -structure, 蟽 -open sets, discuss the properties of 蟽 -open sets, define 蟽 -continuous mappings, (蟽 _ S _ 1, 蟽 _ S _ 2) -continuous mappings with 蟽 -open sets, and study their related properties. In Chapter 3, on the basis of 蟽 -space, we define 蟽 -TSP 0 space, 蟽 T class 1 space, 蟽 T class 2 space, 蟽 T T 3 space, 蟽 -TT 4 space and 蟽 -D0 space, 蟽 -D1 space, 蟽 -D2 space, 蟽 -R201 space, 蟽 -RV 1 space, and further study their properties.
【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

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