本文選題：σ-結(jié)構(gòu) + σ-開(kāi)集��； 參考：《南京師范大學(xué)》2017年碩士論文

【摘要】：2013年,Y. K. Kim和W. K. Min在廣義拓?fù)涞幕A(chǔ)上定義了 σ-結(jié)構(gòu),σ-開(kāi)集,并在此基礎(chǔ)上討論了σ-結(jié)構(gòu)的一些性質(zhì)和擬擴(kuò)充運(yùn)算,而且得到了一些有趣的結(jié)果.本文在上述研究的基礎(chǔ)上進(jìn)一步給出了σ-連續(xù)映射,(σ_1,σ_2) 連續(xù)映射定義以及σ-分離性,D_σ-分離性的定義,并且研究了它們的相關(guān)性質(zhì).具體來(lái)說(shuō),在第一章里,我們介紹了 σ-結(jié)構(gòu)產(chǎn)生的背景,研究發(fā)展概況,同時(shí)介紹了論文中所用到的主要定義定理和相關(guān)的符號(hào).在第二章里,我們首先給出了 σ-結(jié)構(gòu),σ-開(kāi)集的定義,討論了σ-開(kāi)集的性質(zhì),用σ-開(kāi)集定義了 σ-連續(xù)映射,(σ_1,σ_2)-連續(xù)映射,并且研究了它們的相關(guān)性質(zhì).在第三章里,我們?cè)讦?空間的基礎(chǔ)上定義了σ-T_0空間,σ-T_1空間,σ-T_2空間,σ-T_3空間,σ-T_4空間以及σ-D_0空間,σ-D_1空間,σ-D_2空間,σ-R_0空間,σ-R_1空間,并且進(jìn)一步研究了他們的性質(zhì).
[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.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O189.11

【參考文獻(xiàn)】

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

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本文編號(hào)：2109248