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Generalizations of Metric Spaces

  • Michel Marie Deza
  • Elena Deza

Abstract

Some immediate generalizations of the notion of metric, for example, quasi-metric, near-metric, extended metric, were defined in Chap.  1. Here we give some generalizations in the direction of Topology, Probability, Algebra, etc.

Keywords

Fuzzy Number Coxeter Group Hermitian Operator Uniform Space Unital Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [Beer99]
    Beer G. On Metric Boundedness Structures, Set-Valued Anal., Vol. 7, pp. 195–208, 1999. zbMATHCrossRefMathSciNetGoogle Scholar
  2. [DeDu03]
    Deza M.M. and Dutour M. Cones of Metrics, Hemi-metrics and Super-metrics, Ann. of European Academy of Sci., pp. 141–162, 2003. Google Scholar
  3. [Mart00]
    Martin K. A Foundation for Computation, Ph.D. Thesis, Tulane University, Department of Mathematics, 2000. Google Scholar
  4. [ScSk83]
    Schweizer B. and Sklar A. Probabilistic Metric Spaces, North-Holland, Amsterdam, 1983. zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michel Marie Deza
    • 1
  • Elena Deza
    • 2
  1. 1.École Normale SupérieureParisFrance
  2. 2.Moscow State Pedagogical UniversityMoscowRussia

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