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

  1. 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.
  2. 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.

See also