內容提要
Thisisatopologybookforundergraduates
基本拓撲學(英)本書為全英文版。
編輯推薦
Thisisatopologybookforundergraduates,andinwritingitIhavehadtwoaimsinmind.Firstly,tomakesurethestudentseesavarietyofdefferenttechniquesandapplicationsinvolvingpointset,geometric,andalgebraictopology,withoutcelvingtoodeeplyintoanyparticulararea.Secondly,todevelopthereader'sgeometricalinsight;topologyisafterallabranchofgeometry.
目錄
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
