# Normed space

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In mathematics, a **normed space** is a vector space that is endowed with a norm. A complete normed space is called a Banach space.

## Examples of normed spaces

- The Euclidean space endowed with the Euclidean norm for all . This is the canonical example of a
*finite dimensional*vector space; in fact*all*finite dimensional real normed spaces of dimension*n*are isomorphic to this space and, indeed, to one another. - The space of the equivalence class of all real valued bounded Lebesgue measurable functions on the interval [0,1] with the norm . This is an example of an
*infinite dimensional*normed space.