内容提要

编辑推荐

目录

作者：（英）阿姆斯壮　著

ISBN：10位［750628345X］13位［9787506283458］

出版社：世界图书出版公司

出版日期：2007-1-1

定价：￥36.00元

内容提要

Thisisatopologybookforundergraduates,andinwritingitIhavehadtwoaimsinmind.Firstly,tomakesurethestudentseesavarietyofdefferenttechniquesandapplicationsinvolvingpointset,geometric,andalgebraictopology,withoutcelvingtoodeeplyintoanyparticulararea.Secondly,todevelopthereader'sgeometricalinsight;topologyisafterallabranchofgeometry.

本书为全英文版。

编辑推荐

Thisisatopologybookforundergraduates,andinwritingitIhavehadtwoaimsinmind.Firstly,tomakesurethestudentseesavarietyofdefferenttechniquesandapplicationsinvolvingpointset,geometric,andalgebraictopology,withoutcelvingtoodeeplyintoanyparticulararea.Secondly,todevelopthereader'sgeometricalinsight;topologyisafterallabranchofgeometry.

目录

Preface

Chapter1Introduction

1.Euler'stheorem

2.Topologicalequivalence

3.Surfaces

4.Abstractspaces

5.Aclassificationtheorem

6.Topologicalinvariants

Chapter2Continuity

1.Openandclosedsets

2.Continuousfunctions

3.Aspace-fillingcurve

4.TheTietzeextensiontheorem

Chapter3Compactnessandconnectedness

1.ClosedboundedsubsetsofE"

2.TheHeine-Boreltheorem

3.Propertiesofcompactspaces

4.Productspaces

5.Connectedness

6.Joiningpointsbypaths

Chapter4Identificationspaces

1.ConstructingaM/Sbiusstrip

2.Theidentificationtopology

3.Topologicalgroups

4.Orbitspaces

Chapter5Thefundamentalgroup

1.Homotopicmaps

2.Constructionofthefundamentalgroup

3.Calculations

4.Homotopytype

5.TheBrouwerfixed-pointtheorem

6.Separationoftheplane

7.Theboundaryofasurface

Chapter6Triangulations

1.Triangulatingspaces

2.Barycentricsubdivision

3.Simplicialapproximation

4.Theedgegroupofacomplex

5.Triangulatingorbitspaces

6.Infinitecomplexes

Chapter7Surfaces

1.Classification

2.Triangulationandorientation

3.Eulercharacteristics

4.Surgery

5.Surfacesymbols

Chapter8Simplicialhomology

1.Cyclesandboundaries

2.Homologygroups

3.Examples

4.Simplicialmaps

5.Stellarsubdivision

6.Invariance

Chapter9DegreeandLefschetznumber

1.Mapsofspheres

2.TheEuler-Poincar6formula

3.TheBorsuk-Ulamtheorem

4.TheLefschetzfixed-pointtheorem

5.Dimension

Chapter10Knotsandcoveringspaces

1.Examplesofknots

2.Theknotgroup

3.Seifertsurfaces

4.Coveringspaces

5.TheAlexanderpolynomial

Appendix:Generatorsandrelations

Index