基本拓扑学

出版时间：2008-1  出版社：世界图书出版公司  作者：M. A. Armstrong  页数：251  
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内容概要

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. 　　本书为全英文版。

书籍目录

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

用户评论 (总计15条)

•   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。