本文選題：寬球包 + 緊球包��； 參考：《哈爾濱理工大學(xué)》2017年碩士論文

【摘要】：自從Meissner在1911年首次給出完備集的概念,有關(guān)完備集及其特征性質(zhì)的問題一直受到學(xué)者們的廣泛關(guān)注。完備集及其特征性質(zhì)的研究不僅在實(shí)際應(yīng)用中具有重要意義,而且在理論研究上具有一定的挑戰(zhàn)。本文主要在(實(shí))拓?fù)渚�性空間中,關(guān)于給定凸體的完備集及其一些性質(zhì)進(jìn)行研究。首先,給出了在拓?fù)渚�性空間中有界集關(guān)于給定凸體的直徑和外徑的定義�；谟薪缂P(guān)于給定凸體的直徑和外徑的定義,討論了在拓?fù)渚�性,空間中有界集關(guān)于給定凸體的直徑和外徑的相關(guān)結(jié)論。其次,基于在實(shí)拓?fù)渚�性空間中有界集關(guān)于給定凸體的寬球包與緊球包、伴隨變換和半徑函數(shù)的定義,討論有界集關(guān)于給定凸體的寬球包與緊球包、伴隨變換和半徑函數(shù)的有關(guān)性質(zhì),并在此基礎(chǔ)上,討論有界集關(guān)于給定凸體完備的充要條件,和有界集關(guān)于給定凸體有唯一完備化集的條件。再次,基于J.P.Moreno和R.Schneider提出的(K,u)-完備集的概念,本文重新定義(K,u)-完備集的概念,并討論在實(shí)拓?fù)渚�性空間中(K,u)-完備集和唯一完備化集的關(guān)系。最后,基于Papini和吳森林給出的在Banach空間中完備化集的構(gòu)造方法,給出在實(shí)拓?fù)渚�性空間中有界集關(guān)于給定凸體完備化的方法。同時(shí)在Eggleston構(gòu)造完備化集的方法的基礎(chǔ)上,在有限維的Banach空間中給出構(gòu)造完備化集的方法。
[Abstract]:Since the concept of Meissner for the first time in 1911 are complete sets, some properties and characteristics of the complete set of problems has attracted wide attention of scholars. Study on properties of complete sets and features not only have important significance in the practical application, but also has certain challenge in theoretical research. This paper mainly in the (real) linear topological space. Research on complete set for a given convex body and some of its properties. Firstly, gives the definition of boundary in diameter and diameter of a given convex body in topological linear space. Based on bounded sets for a given convex body diameter and diameter of the definition, discusses the related conclusions in topological linear, bounded set diameter and outside for a given convex space. Secondly, based on the real topological linear space bounded sets in a given convex body width and tight bag bag, with the definition of the transformation function and radius, discussion Bounded set for a given convex body width and tight bag bag, with the nature of transformation and function of radius, and on this basis, to discuss the bounded set of sufficient and necessary conditions for a given convex body complete, and bounded set has only one complete set of conditions for a given convex body. Thirdly, based on J.P.Moreno and the R.Schneider (K, U) - the concept of complete set, this paper redefines the concept of (K, U) - complete sets, and discuss in real linear topological space (K, U) - complete set and only complete sets. Finally, methods to construct the complete set in Banach space Papini and Wu Senlin are given based on bounded sets for a given convex completion method in real linear topological space. At the same time in the Eggleston construction method based on the complete set, set of methods is given to construct complete in a finite dimensional Banach space.

【學(xué)位授予單位】：哈爾濱理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O189.11

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