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Elements of The Topology of Plane Sets of Pointspdf电子书版本下载
- M.H.A.Newman 著
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- 出版时间：未知
- 标注页数：221页
- 文件大小：49MB
- 文件页数：228页
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图书目录
PART Ⅰ．GENERAL PROPERTIES OF SETS OF POINTS 1
Chapter Ⅰ．SETS 3
1．Calculus of sets 3
2．Enumerable and non-enumerable sets 12
Chapter Ⅱ．CLOSED SETS AND OPEN SETS IN METRIC SPACES 19
1．Limit point and closure．Closed and open sets 19
2．Convergent sequences of points 32
3．Compact sets 36
4．Induced structure．Relative and absolute properties 42
Chapter Ⅲ．HOMOEOMORPHISM AND CONTINUOUS MAPPINGS 45
1．Equivalent metrics．Topological spaces．Homoeomorphism 45
2．Continuous mappings 56
Chapter Ⅳ．CONNECTION 62
1．Connected sets 62
2．Components 67
3．Connection in compact sets 71
4．Local connection 75
5．Topological characterisation of segment and circle 79
PART Ⅱ．TOPOLOGY OF PLANE SETS OF POINTS 89
Chapter Ⅴ．SEPARATION THEOREMS 91
1．Complexes on a grating 91
2．Alexander＇s Lemma and Jordan＇s Theorem 99
3．Invariance of dimension number and of open sets 114
4．Further separation theorems 116
5．Extension to sets of points in Zp and Rp 121
Chapter Ⅵ．SIMPLY CONNECTED DOMAINS 131
1．Definitions and simple properties 131
2．Mapping on a standard domain 136
3．Paths and deformations 142
Chapter Ⅶ．ACCESSIBILTY AND JORDAN DOMAINS 157
1．Uniform local connection．Accessible points 157
2．Topological mapping of Jordan domains and their closures 165
3．Converse of Jordan＇s Theorem 170
4．Boundary elements．Accessibility and local connection 173
Chapter Ⅷ．CONNEOTIVITY PROPERTIES 188
1．Open sets 188
2．Curved complexes 194
Notes 200
Index 217