強(qiáng)模糊范數(shù)所誘導(dǎo)的模糊化拓?fù)?/H1>
發(fā)布時(shí)間：2019-05-07 11:50
【摘要】：模糊賦范線性空間理論是模糊分析學(xué)的重要組成部分,模糊賦范空間中的拓?fù)浣Y(jié)構(gòu)一直成為眾多學(xué)者的關(guān)注熱點(diǎn).基于強(qiáng)模糊度量空間,本文對(duì)強(qiáng)模糊賦范空間中的模糊化拓?fù)溥M(jìn)行了較為細(xì)致的研究,主要內(nèi)容如下:一、引入強(qiáng)模糊賦范線性空間的概念,給出強(qiáng)模糊賦范空間上具有層次結(jié)構(gòu)的分明拓?fù)渥?并利用此分明拓?fù)渥宕_定強(qiáng)模糊賦范空間上的模糊化拓?fù)?證明了模糊化拓?fù)渑c線性運(yùn)算的相容性.給出了強(qiáng)模糊賦范線性空間序列收斂度的模糊范數(shù)式刻畫(huà),利用序列收斂度的概念,給出了模糊化拓?fù)渑c線性運(yùn)算相容性的另一種證明.研究了強(qiáng)模糊賦范線性空間中映射的連續(xù)性問(wèn)題.二、給出了有限個(gè)模糊賦范線性空間乘積模糊范數(shù)的兩種定義,證明了兩種模糊范數(shù)確定的拓?fù)涞葍r(jià).引入了可數(shù)個(gè)模糊賦范線性空間乘積的定義,研究了可數(shù)個(gè)模糊賦范乘積空間的拓?fù)浣Y(jié)構(gòu).特別地,證明了有限個(gè)強(qiáng)模糊賦范乘積空間確定的模糊化拓?fù)涞扔谄湟蜃涌臻g模糊化拓?fù)涑朔e,可數(shù)個(gè)強(qiáng)模糊賦范乘積空間確定的模糊化拓?fù)鋸?qiáng)于其因子空間模糊化拓?fù)涑朔e.
[Abstract]:The theory of fuzzy normed linear space is an important part of fuzzy analysis. The topological structure of fuzzy normed space has always been the focus of many scholars. Based on strong fuzzy metric space, the fuzzy topology in strongly fuzzy normed space is studied in detail. The main contents are as follows: first, the concept of strongly fuzzy normed linear space is introduced. An explicit topological family with hierarchical structure on strongly fuzzy normed spaces is given, and the fuzzy topology on strongly fuzzy normed spaces is determined by using this distinct topological family. The compatibility between fuzzy topology and linear operation is proved. In this paper, the fuzzy norm formula of convergence degree of strongly fuzzy normed linear space is given. By using the concept of convergence degree of sequence, another proof of compatibility between fuzzy topology and linear operation is given. The continuity of mappings in strongly fuzzy normed linear spaces is studied. Secondly, two definitions of the product fuzzy norm of finite fuzzy normed linear spaces are given, and the topological equivalence of the two fuzzy norms is proved. In this paper, the definition of product of countable fuzzy normed linear spaces is introduced, and the topological structure of countable fuzzy normed product spaces is studied. In particular, it is proved that the fuzzy topology of finite strong fuzzy normed product spaces is equal to the fuzzy topological product of its factor space, and the fuzzy topology of countable strong fuzzy normed product space is stronger than the fuzzy topological product of its factor space.
【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)】：O177
【參考文獻(xiàn)】
相關(guān)期刊論文 前1條
1 吳從p，
本文編號(hào)：2471053
本文鏈接：http://sikaile.net/kejilunwen/yysx/2471053.html
[Abstract]:The theory of fuzzy normed linear space is an important part of fuzzy analysis. The topological structure of fuzzy normed space has always been the focus of many scholars. Based on strong fuzzy metric space, the fuzzy topology in strongly fuzzy normed space is studied in detail. The main contents are as follows: first, the concept of strongly fuzzy normed linear space is introduced. An explicit topological family with hierarchical structure on strongly fuzzy normed spaces is given, and the fuzzy topology on strongly fuzzy normed spaces is determined by using this distinct topological family. The compatibility between fuzzy topology and linear operation is proved. In this paper, the fuzzy norm formula of convergence degree of strongly fuzzy normed linear space is given. By using the concept of convergence degree of sequence, another proof of compatibility between fuzzy topology and linear operation is given. The continuity of mappings in strongly fuzzy normed linear spaces is studied. Secondly, two definitions of the product fuzzy norm of finite fuzzy normed linear spaces are given, and the topological equivalence of the two fuzzy norms is proved. In this paper, the definition of product of countable fuzzy normed linear spaces is introduced, and the topological structure of countable fuzzy normed product spaces is studied. In particular, it is proved that the fuzzy topology of finite strong fuzzy normed product spaces is equal to the fuzzy topological product of its factor space, and the fuzzy topology of countable strong fuzzy normed product space is stronger than the fuzzy topological product of its factor space.
【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)】：O177
【參考文獻(xiàn)】
相關(guān)期刊論文 前1條
1 吳從p，
本文編號(hào)：2471053
本文鏈接：http://sikaile.net/kejilunwen/yysx/2471053.html
最近更新
教材專(zhuān)著
