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
MetricThis entry contributed by Margherita Barile
Explore with Wolfram|Alpha
WolframAlpha
References
Kelley, J. L. General Topology. New York: Van Nostrand, 1955.Referenced on Wolfram|Alpha
PseudometricCite this as:
Barile, Margherita. "Pseudometric." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Pseudometric.html