《Elements of The Topology of Plane Sets of Points》

作者 M.H.A.Newman 编者
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Elements of The Topology of Plane Sets of Points PDF电子版封面 M.H.A.Newman

PART Ⅰ．GENERAL PROPERTIES OF SETS OF POINTS1

Chapter Ⅰ．SETS3

1．Calculus of sets3

2．Enumerable and non-enumerable sets12

Chapter Ⅱ．CLOSED SETS AND OPEN SETS IN METRIC SPACES19

1．Limit point and closure．Closed and open sets19

2．Convergent sequences of points32

3．Compact sets36

4．Induced structure．Relative and absolute properties42

Chapter Ⅲ．HOMOEOMORPHISM AND CONTINUOUS MAPPINGS45

1．Equivalent metrics．Topological spaces．Homoeomorphism45

2．Continuous mappings56

Chapter Ⅳ．CONNECTION62

1．Connected sets62

2．Components67

3．Connection in compact sets71

4．Local connection75

5．Topological characterisation of segment and circle79

PART Ⅱ．TOPOLOGY OF PLANE SETS OF POINTS89

Chapter Ⅴ．SEPARATION THEOREMS91

1．Complexes on a grating91

2．Alexander＇s Lemma and Jordan＇s Theorem99

3．Invariance of dimension number and of open sets114

4．Further separation theorems116

5．Extension to sets of points in Zp and Rp121

Chapter Ⅵ．SIMPLY CONNECTED DOMAINS131

1．Definitions and simple properties131

2．Mapping on a standard domain136

3．Paths and deformations142

Chapter Ⅶ．ACCESSIBILTY AND JORDAN DOMAINS157

1．Uniform local connection．Accessible points157

2．Topological mapping of Jordan domains and their closures165

3．Converse of Jordan＇s Theorem170

4．Boundary elements．Accessibility and local connection173

Chapter Ⅷ．CONNEOTIVITY PROPERTIES188

1．Open sets188

2．Curved complexes194

Notes200

Index217

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