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Introduction To Topology2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

Introduction To Topology
  • Solomon Lefschetz 著
  • 出版社： Princeton University Press
  • ISBN：
  • 出版时间：1949
  • 标注页数：218页
  • 文件大小：53MB
  • 文件页数：226页
  • 主题词：

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图书目录

Introduction,a Survey of Some Topological Concepts3

1．Theory of Sets．Topological Spaces3

2．Questions Related to Curves5

3．Polyhedra8

4．Coincidences and Fixed Points14

5．Vector Fields17

6．Integration and Topology19

Chapter Ⅰ．Basic Information about Sets,Spaces,Vectors,Groups26

1．Questions of Notation and Terminology26

2．Euclidean Spaces,Metric Spaces,Topological Spaces28

3．Compact Spaces34

4．Vector Spaces38

5．Products of Sets,Spaces and Groups．Homotopy40

Problems43

Chapter Ⅱ．Two-dimensional Polyhedral Topology45

1．Elements of the Theory of Complexes．Geometric Consideration45

2．Elements of the Theory of Complexes．Modulo Two Theory50

3．The Jordan Curve Theorem61

4．Proof of the Jordan Curve Theorem65

5．Some Additional Properties of Complexes68

6．Closed Surfaces．Generalities72

7．Closed Surfaces．Reduction to a Normal Form83

Problems84

Chapter Ⅲ．Theory of Complexes86

1．Intuitive Approach86

2．Simplexes and Simplicial Complexes87

3．Chains,Cycles,Homology Groups89

4．Geometric Complexes95

5．Calculation of the Betti Numbers．The Euler-Poincaré Characteristic99

6．Relation between Connectedness and Homology103

7．Circuits105

Problems107

Chapter Ⅳ．Transformations of Complexes．Simplicial Approximations and Related Questions110

1．Set-transformations．Chain-mappings110

2．Derivation112

3．The Brouwer Fixed Point Theorem117

4．Simplicial Approximation119

5．The Brouwer Degree124

6．Hopf＇s Classification of Mappings of n-spheres on n-spheres132

7．Some Theorems on the Sphere134

Problems140

Chapter Ⅴ．Further Properties of Homotopy．Fixed Points．Fundamental Group．Homotopy Groups142

1．Homotopy of Chain-mappings142

2．Homology in Polyhedra．Relation to Homotopy148

3．The Lefschetz Fixed Point Theorem for Polyhedra153

4．The Fundamental Group157

5．The Homotopy Groups170

Problems180

Chapter Ⅵ．Introduction to Manifolds．Duality Theorems183

1．Differentiable and Other Manifolds183

2．The Poincare Duality Theorem188

3．Relative Homology Theory195

4．Relative Manifolds and Related Duality Theory(Elementary Theory)．Alexander＇s Duality Theorem202

Problems206

Bibliography208

List of Symbols211

Index213

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