本文選題：拓撲空間　切入點：算子半群　出處：《內(nèi)蒙古大學》2017年碩士論文　論文類型：學位論文

【摘要】：根據(jù)Olga Ladyzhenskaya在完備距離空間上定義的算子半群的全局吸引子及全局B-吸引子,將它們推廣到Hausdorff拓撲空間上,研究在Hausdorff拓撲空間上算子半群的全局吸引子.我們注意到全局B-吸引子被定義為吸引完備距離空間中每個有界集,而在拓撲空間上沒有有界集的定義,故我們采用相對緊集代替距離空間中的有界集定義了全局C-吸引子和采用基本有界集代替有界集定義了全局S-吸引子.且根據(jù)基本有界集定義了基本(?)類算子半群.并通過結合拓撲學知識,采用夏道行關于笛卡爾定向集的思想方法和網(wǎng)的收斂的概念,研究極限集,這對給出拓撲空間中算子半群吸引子的相關概念起到了關鍵作用.本文首先得到了拓撲空間上算子半群的全局吸引子、全局C-吸引子和全局s-吸引子的存在條件.例如,證明了定義在Hausdorff拓撲空間上算子半群{Vt},如果{Vt}有有限的全局吸收集B0,則{Vt}有非空極小的緊不變?nèi)治覯 =σ-(B0);如果{V1}有相對緊的全局C-吸收集C0,則{V,}有非空極小的緊不變?nèi)諧-吸引子MC=σ(C0);如果{Vf}是基本(?)類半群,有基本有界的全局s-吸收集S0,則{Vt}有非空極小的緊不變?nèi)謘-吸引子Ms=σ(s0).然后,討論了極小緊的全局吸引子、極小緊的全局C-吸引子和極小緊的全局s-吸引子存在的充分條件.最后,給出了Hausdorff拓撲空間中極小緊吸引集的連通性定理,得到了這三類全局吸引子的連通性結論.
[Abstract]:According to the global attractor and global attractor of B- operator Olga Ladyzhenskaya is defined in the complete metric space of semigroups, extending them to the Hausdorff topological space, study on the global attractor operator in Hausdorff topological space semigroups. We note that the global attractor B- is defined for each attraction in complete metric spaces and bounded set, and in there is no definition of topological space bounded set, so we adopt relatively compact set instead of distance space bounded set in the definition of the global attractor and C- using basic bounded set instead of bounded set S- and the definition of the global attractor. According to the basic definition of bounded set of basic (?) - Semigroups and through. Combining the topology knowledge concept by Xia's thought about the method and Descartes directed set the convergence, the research limit set, the related concept of attractor Operator Semigroups in topological space are To play a key role. This paper firstly obtained topological space Semigroups of global attractor, conditions for the existence of global attractor and a global attractor of the C- s-. For example, the proof of the Hausdorff topological space of operator semigroup {Vt}, if {Vt} has limited absorbing set B0, then {Vt} has a non empty Compact Minimal invariant global attractor M = sigma (B0); if {V1} has a global C- relatively compact absorption set C0, {V,} has a nonempty minimal invariant global attractor of MC= Sigma C- (C0); if {Vf} is a basic (?) semigroups, a basic global s- sector absorbing collection S0 {Vt}, a non empty minimal invariant global attractor Ms= Sigma s- (S0). Then, discusses the global attractor minimal compact, sufficient conditions for the existence of the global attractor and minimal compact C- minimal compact global s- attractor. Finally, gives the Hausdorff topological space minimum connectivity theorem of compact attractor, The connectedness of the three kinds of global attractors is obtained.

【學位授予單位】：內(nèi)蒙古大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O189.11

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