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Foreword

Preface

Preface to the English Edition

Chapter 1 The origin of generalized metric spaces

1,1 Notations and terminologies

1.2 Distance functions

1.3 Bases

1.4 Stratifications

1.5 Networks and (rood k)-networks

1.6 k-networks and weak bases

1.7 Generalized countably compact spaces

1.8 Examples

Chapter 2 Mappings on metric spaces

2.1 Classes of mappings

2.2 Perfect mappings

2.3 Quotient mappings

2.4 Open mappings

2.5 Closed mappings

2.6 Compact-covering mappings

2.7 s-mappings

2.8 ss-mappings

2.9 7r-mappings

2.10 Compact mappings

2.11 a-locally finite mappings

Chapter 3 Generalized metric spaces

3.1 Spaces with point-countable covers

3.2 Z-spaces

3.3 a-spaces and semi-stratifiable spaces

3.4 k-semi-stratifiable spaces

3.5 Mi-spaces

3.6 Developable spaces and p-spaces

3.7 M-spaces

3.8 R-spaces

3.9 g-metrizable spaces

3.10 Open questions

Appendix A Characterizations of several covering properties

A.1 Paracompact spaces

A.2 Metacompact spaces

A.3 Subparacompact spaces

A.4 Submetacompact spaces

A.5 Meta-LindelSf spaces

Appendix B The formation of the theory of generalized metric spaces

B.1 A historical review

B.2 The foundation laying period

B.3 The formation period

Bibliography

Index

Mathematics Monograph Series

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