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Book Categories |
Preface | ||
Ch. 1 | Introduction to topology | 1 |
1.1 | An overview | 1 |
Ch. 2 | Point-set topology in R[superscript n] | 7 |
2.1 | Open and closed sets in R[superscript n] | 7 |
2.2 | Relative neighborhoods | 16 |
2.3 | Continuity | 19 |
2.4 | Compact sets | 26 |
2.5 | Connected sets | 29 |
2.6 | Applications | 31 |
Ch. 3 | Point-set topology | 36 |
3.1 | Open sets and neighborhoods | 36 |
3.2 | Continuity, connectedness, and compactness | 42 |
3.3 | Separation axioms | 46 |
3.4 | Product spaces | 47 |
3.5 | Quotient spaces | 51 |
Ch. 4 | Surfaces | 55 |
4.1 | Complexes | 55 |
4.2 | Surfaces | 64 |
4.3 | Triangulations | 73 |
4.4 | Classification of surfaces | 79 |
4.5 | Surfaces with boundary | 86 |
Ch. 5 | The euler characteristic | 90 |
5.1 | Topological invariants | 90 |
5.2 | Graphs and trees | 91 |
5.3 | The euler characteristic and the sphere | 97 |
5.4 | The euler characteristic and surfaces | 104 |
5.5 | Map-coloring problems | 109 |
Ch. 6 | Homology | 116 |
6.1 | The algebra of chains | 117 |
6.2 | Homology | 128 |
6.3 | More computations | 139 |
6.4 | Betti numbers and the euler characteristic | 141 |
Ch. 7 | Cellular functions | 144 |
7.1 | Cellular functions | 144 |
7.2 | Homology and cellular functions | 152 |
7.3 | Examples | 157 |
7.4 | Covering spaces | 162 |
Ch. 8 | Invariance of homology | 170 |
8.1 | Invariance of homology for surfaces | 170 |
8.2 | The Simplicial Approximation Theorem | 174 |
Ch. 9 | Homotopy | 184 |
9.1 | Homotopy and homology | 184 |
9.2 | The fundamental group | 190 |
Ch. 10 | Miscellany | 199 |
10.1 | Applications | 199 |
10.2 | The Jordan Curve Theorem | 208 |
10.3 | 3-manifolds | 212 |
Ch. 11 | Topology and calculus | 221 |
11.1 | Vector fields and differential equations in R[superscript n] | 221 |
11.2 | Differentiable manifolds | 233 |
11.3 | Vector fields on manifolds | 234 |
11.4 | Integration on manifolds | 241 |
Appendix: Groups | 247 | |
References | 256 | |
Index | 258 |
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Add Topology of Surfaces, This book aims to provide undergraduates with an understanding of geometric topology. Topics covered include a sampling from point-set, geometric, and algebraic topology. The presentation is pragmatic, avoiding the famous pedagogical method whereby one b, Topology of Surfaces to the inventory that you are selling on WonderClubX
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Add Topology of Surfaces, This book aims to provide undergraduates with an understanding of geometric topology. Topics covered include a sampling from point-set, geometric, and algebraic topology. The presentation is pragmatic, avoiding the famous pedagogical method whereby one b, Topology of Surfaces to your collection on WonderClub |