Category:Supremum Norm

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This category contains results about Supremum Norm.

Let $S$ be a set.

Let $\struct {X, \norm {\,\cdot\,} }$ be a normed vector space.

Let $\BB$ be the set of bounded mappings $S \to X$.


For $f \in \BB$ the supremum norm of $f$ on $S$ is defined as:

$\norm f_\infty = \sup \set {\norm {\map f x}: x \in S}$