基本拓扑学

2008-1  

世界图书出版公司  

M. A. Armstrong  

251  

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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. 　　本书为全英文版。

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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基本拓扑学 PDF格式下载

详细的讲解与精当的编排使得本书成为一本拓扑学入门的经典

这本书不拘泥于技术细节但是对于拓扑学整体上把握很好，对于训练拓扑直观很有帮助

这本书处理一些拓扑问题有独特的方法，还是不错的

非常经典的一本书，值得多看几遍

非常新，讲解清晰，初学不错

朋友孩子要的，课外补充读物，需要的

很经典的入门图书，值得一看！

数学的魅力你懂的

国内最好的是北大的，国外最好的拓扑入门书就这本了，非常经典！！

比较重视直观，是很好的入门教材

good introduction to topology

影印版还算清晰

这是一本很好的教材，最然比较老，但很经典。写得很人性化，也把各种概念解释的很透彻。

还好，不过影印版就是纸质不太好~

不是国外最好的教材。有些讲得不是很清楚。