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Pseudometric


A distance g on a set that fulfils the same properties as a metric except relaxes the definition to allow the distance between two different points to be zero.

An example of pseudometric on the set of all functions phi:R->R is defined by g(phi,psi)=|phi(0)-psi(0)|. It is nonnegative, symmetric, fulfils the triangle inequality and the condition g(phi,phi)=0, but it is also true that g(sin,sin^2)=0.


See also

Metric

This entry contributed by Margherita Barile

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References

Kelley, J. L. General Topology. New York: Van Nostrand, 1955.

Referenced on Wolfram|Alpha

Pseudometric

Cite this as:

Barile, Margherita. "Pseudometric." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Pseudometric.html

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