Topics in TopologyPDF电子书下载

Chapter Ⅰ．POLYTOPFS 1

1．Affine Simplexes and Complexes 1

2．Geometric Complexes 9

3．Comparison of the Topologies Associated with Affine Complexes 16

Chapter Ⅱ．SINGULAR COMPLEXES 23

Chapter Ⅲ．MAPPING AND IMBEDDING THEOREMS．RETRACTION 35

1．Fundamental Mapping Theorem 35

2．Application to Normal and Tychonoff Spaces 45

3．Compact Imbedding of Separable Metric Spaces 49

4．Topological Imbedding in Euclidean Spaces 53

5．Retraction 58

Chapter Ⅳ．LOCAL CONNECTEDNESS AND RELATED TOPICS 75

1．Localization 75

2．Partial Realization of Complexes．Application to Local Connectedness 81

3．Relations Between the LC Properties and Retraction 92

4．Characterization of the LC Properties by Mappings of Continuous Complexes 98

5．Homology Theory of LC Spaces 104

6．Coincidences and Fixed Points 112

7．HLC Spaces．Generalized Manifolds 123

Special Bibliography 127

General Bibliography 133

Index 136