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ELEMENTARY TOPOLOGY AND APPLICATIONSPDF|Epub|txt|kindle电子书版本网盘下载
- 著
- 出版社： WORLD SCIENTIFIC
- ISBN：9810242409
- 出版时间：2000
- 标注页数：201页
- 文件大小：20MB
- 文件页数：210页
- 主题词：
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图书目录
CHAPTER 0. SETS AND NUMBERS1
0.1 Rudiments of Logic1
0.2 Fundamentals of Set Description5
0.3 Set Inclusion and Equality5
0.4 An Axiom System for Set Theory6
0.5 Unions and Intersections6
0.6 Set Difference7
0.7 Integers and Induction7
0.8 Simple Cartesian Products11
0.9 Relations11
0.10 Functions12
0.11 Sequences14
0.12 Indexing Sets15
0.13 Important Formulas16
0.14 Inverse Functions16
0.15 More Important Formulas17
0.16 Partitions18
0.17 Equivalence Relations, Partitions and Functions18
0.18 General Cartesian Products19
0.19 The Sixth Axiom (Axiom of Choice)20
0.20 Well-Orders and Zorn21
0.21 Yet More Important Formulas22
0.22 Cardinality22
CHAPTER 1. METRIC AND TOPOLOGICAL SPACES31
1.1 Metrics and Topologies31
1.2 Time out for Notation33
1.3 Metrics Generate Topologies35
1.4 Continuous Functions36
1.5 Subspaces39
1.6 Comparable Topologies39
CHAPTER 2. FROM OLD TO NEW SPACES47
2.1 Product Spaces47
2.2 Product Metrics and Topologies51
2.3 Quotient Spaces53
2.4 Applications (Mobius Band, Klein Bottle, Torus, Projective Plane, etc.)55
CHAPTER 3. VERY SPECIAL SPACES67
3.1 Compact Spaces67
3.2 Compactif'ication (One-Point Only)73
3.3 Complete Metric Spaces (Baire-Category, Banach Contraction Theorem and Applications of Roots of y = h(x) to Systems of Linear Equations75
3.4 Connected and Arcwise Connected Spaces80
CHAPTER 4. FUNCTION SPACES89
4.1 Function Space Topologies89
4.2 Completness and Compactness (Ascoli-Arzela Theorem, Picard's Theorem, Peano's Theorem)92
4.3 Approximation (Bernstein's polynomials, Stone-Weierstrass Approximation)100
4.4 Function-Space Functions103
CHAPTER 5. TOPOLOGICAL GROUPS114
5.1 Elementary Structures114
5.2 Topological Isomorphism Theorems121
5.3 Quotient Group Recognition123
5.4 Morphism Groups (Topological and Transformation Groups)124
CHAPTER 6. SPECIAL GROUPS131
6.1 Preliminaries131
6.2 Groups of Matrices134
6.3 Groups of Isometries135
6.4 Relativity and Lorentz Transformations140
CHAPTER 7. NORMALITY AND PARACOMPACTNESS147
7.1 Normal Spaces (Urysohn's Lemma)147
7.2 Paracompact Spaces (Partitions of Unity with and Application to Embedding of Manifolds in Euclidean Spaces)151
CHAPTER 8. THE FUNDAMENTAL GROUP167
8.1 Description of II,(X,b)167
8.2 Elementary Facts about II,(X,b)173
8.3 Simplicial Complexes175
8.4 Barycentric Subdivision179
8.5 The Simplicial Approximation181
8.6 The Fundamental Group of Polytopes183
8.7 Graphs and Trees187
APPENDIX A. SOME INEQUALITIES193
APPENDIX B. BINOMIAL EQUALITIES195
LIST OF SYMBOLS197
INDEX199