Contents
Foreword
Preface
Preface to the English Edition
Chapter 1 The origin of generalized metric spaces 1
1.1 Notations and terminologies 2
1.2 Distance functions 5
1.3 Bases 12
1.4 Stratifications 19
1.5 Networks and (mod k)-networks 26
1.6 k-networks and weak bases 30
1.7 Generalized countably compact spaces 37
1.8 Examples 42
Chapter 2 Mappings on metric spaces 55
2.1 Classes of mappings 56
2.2 Perfect mappings 63
2.3 Quotient mappings 74
2.4 Open mappings 82
2.5 Closed mappings 90
2.6 Compact-covering mappings 104
2.7 s-mappings 112
2.8 ss-mappings 122
2.9 π-mappings 131
2.10 Compact mappings 138
2.11 σ-locally finite mappings 150
Chapter 3 Generalized metric spaces 157
3.1 Spaces with point-countable covers 158
3.2 ε-spaces 170
3.3 σ-spaces and semi-stratifiable spaces 192
3.4 k-semi-stratifiable spaces 205
3.5 Mi-spaces 217
3.6 Developable spaces and p-spaces 227
3.7 M-spaces 241
3.8 spaces 250
3.9 g-metrizable spaces 263
3.10 Open questions 269
Appendix A Characterizations of several covering properties 275
A.1 Paracompact spaces 275
A.2 Metacompact spaces 281
A.3 Subparacompact spaces 283
A.4 Submetacompact spaces 286
A.5 Meta-Lindel.of spaces 292
Appendix B The formation of the theory of generalized metric spaces 294
B.1 A historical review 295
B.2 The foundation laying period 296
B.3 The formation period 304
Bibliography 322
Index 348