Definition:Standard Bounded Metric

Theorem
Let $M = \struct {A, d}$ be a metric space.

Let $\bar d: A^2 \to \R$ be the mapping defined as:
 * $\forall \tuple {x, y} \in A^2: \map {\bar d} {x, y} = \min \set {1, \map d {x, y} }$

Then $\bar d$ is known as the standard bounded metric of $d$.

Also see

 * Standard Bounded Metric is Metric