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Homesemimetric

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# semimetric

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

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

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.

Related:

GeneralizationOfAPseudometric

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

54E25*no label found*

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