基本拓?fù)鋵W(xué)

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. 　　本書為全英文版。

書籍目錄

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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