基本拓扑学
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九五品
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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
装帧平装
上书时间2024-10-02
商品详情
- 品相描述:九五品
图书标准信息
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作者
[英]阿姆斯壮 著
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出版社
世界图书出版公司
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出版时间
2008-01
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版次
1
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ISBN
9787506283458
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定价
36.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
251页
- 【内容简介】
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Thisisatopologybookforundergraduates,andinwritingitIhavehadtwoaimsinmind.Firstly,tomakesurethestudentseesavarietyofdefferenttechniquesandapplicationsinvolvingpointset,geometric,andalgebraictopology,withoutcelvingtoodeeplyintoanyparticulararea.Secondly,todevelopthereadersgeometricalinsight;topologyisafterallabranchofgeometry.
本书为全英文版。
- 【目录】
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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
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