semimetric

A semimetric on a set $X$ is a function $d:X\times X\to ℝ$ which satisfies:

1. $d(x,y)\ge 0$

2. $d(x,y)=0$ if and only if $x=y$;

3. $d(x,y)=d(y,x)$.

A semimetric differs from a metric in that the triangle inequality is not required to hold.