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ForewordPrefacePreface to the English EditionChapter 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 ExamplesChapter 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 mappingsChapter 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 questionsAppendix 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 spacesAppendix 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 periodBibliographyIndexMathematics Monograph Series