semimetricSemimetric2004-06-08 21:56:062004-10-02 14:58:49Definition% this is the default PlanetMath preamble. as your knowledge
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\newcommand{\Per}{\operatorname{Per}}A semimetric on a set $X$ is a function $d\colon X\times X\to \R$ which satisfies:
\begin{enumerate}
\item $d(x,y)\geq 0$
\item $d(x,y)= 0$ if and only if $x=y$;
\item $d(x,y) = d(y,x)$.
\end{enumerate}
A semimetric differs from a metric in that the triangle inequality is not required to hold.