Definition:Standard Bounded Metric
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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 $d$.