The Origin of Generalized Metric Spaces

  • Shou LinEmail author
  • Ziqiu Yun
Part of the Atlantis Studies in Mathematics book series (ATLANTISSM, volume 6)


In this chapter, we derive most of the generalized metric spaces that will be discussed in this book from three perspectives: distance functions, bases or their extensions and generalized countable compactness. At the same time, we give some simple characterizations of these spaces, describe their basic operation properties, such as hereditary properties, productive properties and properties preserved under topological sums, and discuss their preliminary relationships with some other classes of spaces.

Copyright information

© Atlantis Press and the author(s) 2016

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsMinnan Normal UniversityZhangzhouChina
  2. 2.Department of MathematicsSoochow UniversitySuzhouChina

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