Let S be a set. By a distance function on S one means a function d(x,y) of pairs of elements of S, with values in the real numbers, satisfying the following conditions:
  • d(x, y)≥ 0 for all x, y∈ S, and = 0 if and only if x = y.

  • d(x, y) = d(y,x) for all x,yS.

  • d(x, y) ≤ d(x, z) + d(z,y) for all x, y, zS.


Vector Space Distance Function Boundary Point Triangle Inequality Open Ball 
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 Science+Business Media New York 1998

Authors and Affiliations

  • Rami Shakarchi
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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