- 作 者：J.M.SINGER J.A.THORPE
- 出 版 社：
- 出版年份：2222
- ISBN：0387902023
- 注意：在使用云解压之前，请认真核对实际PDF页数与内容!
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Chapter 1 Some point set topology 1
1.1 Naive set theory 1
1.2 Topological spaces 5
1.3 Connected and compact spaces 11
1.4 Continuous functions 13
1.5 Product spaces 16
1.6 The Tychonoff theorem 20
Chapter 2 More point set topology 26
2.1 Separation axioms 26
2.2 Separation by continuous functions 31
2.3 More separability 34
2.4 Complete metric spaces 40
2.5 Applications 43
Chapter 3 Fundamental group and covering spaces 49
3.1 Homotopy 49
3.2 Fundamental group 52
3.3 Covering spaces 62
Chapter 4 Simplicial complexes 78
4.1 Geometry of simplicial complexes 79
4.2 Barycentric subdivisions 83
4.3 Simplicial approximation theorem 90
4.4 Fundamental approup of a simplicial complex 94
Chapter 5 Manifolds 109
5.1 Differentiable manifolds 109
5.2 Differential forms 118
5.3 Miscellaneous facts 132
Chapter 6 Homology theory and the De Rham theory 153
6.1 Simplicial homology 153
6.2 De Rham’s theorem 161
Chapter 7 Intrinsic Riemannian geometry of surfaces 175
7.1 Parallel translation and connections 175
7.2 Structural equations and curvature 184
7.3 Interpretation of curvature 190
7.4 Geodesic coordinate systems 198
7.5 Isometries and spaces of constant curvature 207
Chapter 8 Imbedded manifolds in R3 216
Bibliography 230
Index 231