General Definitions

  • Michel Marie Deza
  • Elena Deza

Abstract

Let X be a set. A function d:X×X→ℝ is called a distance (or dissimilarity) on X if, for all x,yX, there holds:
  1. 1.

    d(x,y)≥0 (nonnegativity);

     
  2. 2.

    d(x,y)=d(y,x) (symmetry);

     
  3. 3.

    d(x,x)=0 (reflexivity).

     

Keywords

Chromatic Number Isometric Embedding Geodesic Segment Ultrametric Space Normed Vector Space 
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.

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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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