Category:Supremum Metric

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This category contains results about the supremum metric.
Definitions specific to this category can be found in Definitions/Supremum Metric.

Let $S$ be a set.

Let $M = \left({A', d'}\right)$ be a metric space.

Let $A$ be the set of all bounded mappings $f: S \to M$.

Let $d: A \times A \to \R$ be the function defined as:

$\displaystyle \forall f, g \in A: d \left({f, g}\right) := \sup_{x \mathop \in S} d' \left({f \left({x}\right), g \left({x}\right)}\right)$

where $\sup$ denotes the supremum.

$d$ is known as the supremum metric on $A$.