The idea of mutual classification of spaces and mappings is one of the main research directions
of point set topology. In a systematical way this book discusses the basic theory of
generalized metric spaces by using the mapping method and summarizes the most important
research achievements particularly those from Chinese scholars in the theory of spaces and
mappings since the 1960s. This book has three chapters two appendices and a list of more than
400 references. The chapters are The origin of generalized metric spaces Mappings on metric
spaces and Classes of generalized metric spaces. Graduates or senior undergraduates in
mathematics major can use this book as their text to study the theory of generalized metric
spaces. Researchers in this field can also use this book as a valuable reference.
