Let $(X,d)$ be a [metric space](/page/Metric%20Space), let $f:X \to X$ be a function, and let $c \in [0,1)$. For each nonempty subset $A \subset X$, define the extended diameter of $A$ by
where the supremum is taken in the extended nonnegative real line.
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In expressions of the form $c\,\operatorname{diam}(A)$, use the convention that $c r$ has its usual meaning for $r<\infty$, that $c\infty=\infty$ when $c>0$, and that $0\cdot\infty=0$.