Definition:Scaled Euclidean Metric

Definition

Let $\R_{>0}$ be the set of strictly positive real numbers.

Let $\delta: \R_{>0} \times \R_{>0} \to \R$ be the metric on $\R_{>0}$ defined as:

$\forall x, y \in \R_{>0}: \map \delta {x, y} = \dfrac {\size {x - y} } {x y}$

Then $\delta$ is the scaled Euclidean metric on $\R_{>0}$.

Also see

• Scaled Euclidean Metric is Metric

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $32$. Special Subsets of the Real Line: $10$