Elements of The Topology of Plane Sets of PointsPDF电子书下载

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