# 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 $M = \struct {A', d'}$ 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:

- $\ds \forall f, g \in A: \map d {f, g} := \sup_{x \mathop \in S} \map {d'} {\map f x, \map g x}$

where $\sup$ denotes the supremum.

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

## Subcategories

This category has the following 4 subcategories, out of 4 total.

## Pages in category "Supremum Metric"

The following 16 pages are in this category, out of 16 total.

### S

- Supremum Metric and L1 Metric on Closed Real Intervals are not Topologically Equivalent
- Supremum Metric is Metric
- Supremum Metric on Bounded Continuous Mappings is Metric
- Supremum Metric on Bounded Real Functions on Closed Interval is Metric
- Supremum Metric on Bounded Real Sequences is Metric
- Supremum Metric on Bounded Real-Valued Functions is Metric
- Supremum Metric on Continuous Real Functions is Metric
- Supremum Metric on Continuous Real Functions is Subspace of Bounded
- Supremum Metric on Continuous Real Functions/Examples
- Supremum Metric on Continuous Real Functions/Examples/Closure of Open 1-Ball of 0 on Unit Interval
- Supremum Metric on Differentiability Class is Metric
- Supremum Metric on Differentiability Class/Examples
- Supremum Metric on Differentiability Class/Examples/Difference between C0 and C1
- Supremum Metric on Differentiability Class/Examples/Difference between C0 and C1/Application