Metric Spaces and a Metrization Theorem

  • Gordon Whyburn
  • Edwin Duda
Part of the Undergraduate Texts in Mathematics book series (UTM)


A distance function p in a set X is a nonnegative real-valued function defined for each pair of points x, yX and satisfying:
  1. (i)

    ρ(x, y) = 0 if and only if x = y,

  2. (ii)

    ρ(x, y) = ρ(y, x),

  3. (iii)

    ρ(x, z) < ρ(x, y) + ρ(y, z) (triangle inequality).



Distance Function Limit Point Triangle Inequality Dense Subset Number System 
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  1. Maurice Fréchet, Sur quelques points du calcul fonctionnel, Rendiconti del Circolo Matemático di Palermo, vol. 22 (1906).Google Scholar
  2. P. Urysohn, Über die Metrization der kompakten topologischen Räume, Mathematische Annalen, vol. 92 (1924), pp. 275–293.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Gordon Whyburn
    • 1
  • Edwin Duda
    • 2
  1. 1.DePartment of MathematicsUniversity of VirginiaCharlottesvilleUSA
  2. 2.DePartment of MathematicsUniversity of MiamiCoral GablesUSA

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