Discrete Metric

The metric defined on a nonempty set by

			(1)
			(2)

if for all .

It follows that the open ball of radius and center at

$B(x_0,r)={x in X|g(x_0,x)<r}$

(3)

is

${{x_0} if 0<r<=1; X if r>1.$

(4)

The metric topology induced is the discrete topology.

This entry contributed by Margherita Barile

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Barile, Margherita. "Discrete Metric." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/DiscreteMetric.html

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