基本拓扑学

图书标准信息

• 作者 [英]阿姆斯壮 著
• 出版社 世界图书出版公司
• 出版时间 2008-01
• 版次 1
• ISBN 9787506283458
• 定价 36.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 251页

【内容简介】

Thisisatopologybookforundergraduates,andinwritingitIhavehadtwoaimsinmind.Firstly,tomakesurethestudentseesavarietyofdefferenttechniquesandapplicationsinvolvingpointset,geometric,andalgebraictopology,withoutcelvingtoodeeplyintoanyparticulararea.Secondly,todevelopthereadersgeometricalinsight;topologyisafterallabranchofgeometry.
本书为全英文版。

【作者简介】

M.A.Armstrong，英国杜伦大学（Durham University）数学系教授。

【目录】

Preface
Chapter1Introduction
1.Eulerstheorem
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