semimetric
A semimetric on a set $X$ is a function $d:X\times X\to \mathbb{R}$ 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.
Title  semimetric 

Canonical name  Semimetric 
Date of creation  20130322 14:24:15 
Last modified on  20130322 14:24:15 
Owner  Koro (127) 
Last modified by  Koro (127) 
Numerical id  8 
Author  Koro (127) 
Entry type  Definition 
Classification  msc 54E25 
Related topic  GeneralizationOfAPseudometric 