# semimetric

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

1. 1.

$d(x,y)\geq 0$

2. 2.

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

3. 3.

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

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

Title semimetric Semimetric 2013-03-22 14:24:15 2013-03-22 14:24:15 Koro (127) Koro (127) 8 Koro (127) Definition msc 54E25 GeneralizationOfAPseudometric