關(guān)于M-結(jié)構(gòu)新的分離性及弱M-連續(xù)映射的研究
發(fā)布時間：2018-09-09 18:29
【摘要】：廣義拓撲是一般拓撲的推廣,具有一般拓撲中的一些好的性質(zhì),同時它也極大地豐富和發(fā)展了一般拓撲的研究.1997年,匈牙利數(shù)學(xué)家A.Csaszar首先定義了廣義拓撲,并且研究了廣義拓撲性質(zhì)以及廣義連續(xù),得到了很多有意義的結(jié)果.2012年,A.Al-Omari和T.Noiri定義了M 結(jié)構(gòu).同年,M.Navaneetha-krishnan 和 S.Thamaraiselvi 進一步研究了M-結(jié)構(gòu)的一些性質(zhì).2015年,李中元研究了 M-結(jié)構(gòu)中的分離性和(M1,M2)-連續(xù)映射的性質(zhì),得到了M 結(jié)構(gòu)中很多有用的結(jié)論.本文是在前面學(xué)者研究的基礎(chǔ)上進一步研究了M-結(jié)構(gòu)中新的分離性以及弱M-連續(xù)映射.第一章,我們介紹M-結(jié)構(gòu)產(chǎn)生的具體背景、研究和發(fā)展的概況,同時介紹了論文中要用到的主要定義、定理以及相關(guān)的記號.第二章,我們在M-空間中定義了g -閉集、M-內(nèi)核、M-T1/2空間、并且討論了相關(guān)的一些性質(zhì),同時也在M-R0和M-R1空間中進一步研究了這些分離性的新的一些性質(zhì)和關(guān)系.第三章,我們給出了弱M-連續(xù)映射和弱M-閉包連續(xù)映射定義,并研究了弱M-連續(xù)映射的性質(zhì)以及弱M-連續(xù)映射和弱M-閉包連續(xù)映射的關(guān)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.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O189.11
本文編號：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.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O189.11
【參考文獻】
相關(guān)期刊論文 前1條
1 ;μ-Separations in generalized topological spaces[J];Applied Mathematics:A Journal of Chinese Universities(Series B);2010年02期
相關(guān)碩士學(xué)位論文 前1條
1 李中元;關(guān)于M-結(jié)構(gòu)分離性及（M_1，M_2）-連續(xù)映射的研究[D];南京師范大學(xué);2016年
，本文編號：2233219
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