基本拓?fù)鋵W(xué)

出版時(shí)間:2008-1  出版社:世界圖書(shū)出版公司  作者:M. A. Armstrong  頁(yè)數(shù):251  
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內(nèi)容概要

This is a topology book for undergraduates,and in writing it I have had two aims in mind.Firstly,to make sure the student sees a variety of defferent techniques and applications involving point set,geometric,and algebraic topology,without celving too deeply into any particular area.Secondly,to develop the reader's geometrical insight;topology is after all a branch of geometry.   本書(shū)為全英文版。

書(shū)籍目錄

PrefaceChapter 1  Introduction  1.Euler's theorem  2.Topological equivalence  3.Surfaces  4.Abstract spaces  5.A classification theorem  6.Topological invariantsChapter 2  Continuity  1.Open and closed sets  2.Continuous functions  3.A space-filling curve  4.The Tietze extension theoremChapter 3  Compactness and connectedness  1.Closed bounded subsets of E"  2.The Heine-Borel theorem  3.Properties of compact spaces  4.Product spaces  5.Connectedness  6.Joining points by pathsChapter 4  Identification spaces  1.Constructing a M/Sbius strip  2.The identification topology  3.Topological groups  4.Orbit spacesChapter 5  The fundamental group  1.Homotopic maps  2.Construction of the fundamental group  3.Calculations  4.Homotopy type  5.The Brouwer fixed-point theorem  6.Separation of the plane  7.The boundary of a surfaceChapter 6  Triangulations  1.Triangulating spaces  2.Barycentric subdivision  3.Simplicial approximation  4.The edge group of a complex  5.Triangulating orbit spaces  6.Infinite complexesChapter 7  Surfaces  1.Classification  2.Triangulation and orientation  3.Euler characteristics  4.Surgery  5.Surface symbolsChapter 8  Simplicial homology  1.Cycles and boundaries  2.Homology groups  3.Examples  4.Simplicial maps  5.Stellar subdivision  6.InvarianceChapter 9  Degree and Lefschetz number  1.Maps of spheres  2.The Euler-Poincar6 formula  3.The Borsuk-Ulam theorem  4.The Lefschetz fixed-point theorem  5.DimensionChapter 10  Knots and covering spaces  1.Examples of knots  2.The knot group  3.Seifert surfaces  4.Covering spaces  5.The Alexander polynomialAppendix: Generators and relationsIndex

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用戶(hù)評(píng)論 (總計(jì)15條)

 
 

  •   詳細(xì)的講解與精當(dāng)?shù)木幣攀沟帽緯?shū)成為一本拓?fù)鋵W(xué)入門(mén)的經(jīng)典
  •   這本書(shū)不拘泥于技術(shù)細(xì)節(jié)但是對(duì)于拓?fù)鋵W(xué)整體上把握很好,對(duì)于訓(xùn)練拓?fù)渲庇^(guān)很有幫助
  •   這本書(shū)處理一些拓?fù)鋯?wèn)題有獨(dú)特的方法,還是不錯(cuò)的
  •   非常經(jīng)典的一本書(shū),值得多看幾遍
  •   非常新,講解清晰,初學(xué)不錯(cuò)
  •   朋友孩子要的,課外補(bǔ)充讀物,需要的
  •   很經(jīng)典的入門(mén)圖書(shū),值得一看!
  •   數(shù)學(xué)的魅力你懂的
  •   國(guó)內(nèi)最好的是北大的,國(guó)外最好的拓?fù)淙腴T(mén)書(shū)就這本了,非常經(jīng)典??!
  •   比較重視直觀(guān),是很好的入門(mén)教材
  •   good introduction to topology
  •   影印版還算清晰
  •   這是一本很好的教材,最然比較老,但很經(jīng)典。寫(xiě)得很人性化,也把各種概念解釋的很透徹。
  •   還好,不過(guò)影印版就是紙質(zhì)不太好~
  •   不是國(guó)外最好的教材。有些講得不是很清楚。
 

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