林壽、惲自求主編的《廣義度量空間與映射(英
文版)(精)》介紹了，This is the first book on
generalized metric spaces. The ideas and
problems of thetheory of generalized metric
spaces greatly influenced all domains
ofset-theoretic topology.
A main goal of this book is to describe
the present structure of the theory
ofgeneralized metric spaces and the modem
developments in this theory. The
bookdiscusses the basic theory of
generalized metric spaces by using the
mapping method,and summarizes the important
research achievements since the 1960's
particularly byChinese scholars.
There are three chapters“The Origin of
Generalized Metric Spaces”, “Map-pings on
Metric Spaces”, and “Classes of
Generalized Metric Spaces”. In
additionthere are two appendices of about XX
pages in total, and about 500 references.
The book will be a valuable source of
information for graduate and undergradu-ate
topology students wishing to know more about
this exciting field, or ways it couldbe
applied to other mathematical disciplines.
It will also be very helpful to experts
intopology already working in generalized
metric spaces.

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