An ordered pair \((V,\lVert \cdot\rVert)\) of a vector space \(V\) over \(\mathbb{R}\) or \(\mathbb{C}\) and a norm \(\lVert \cdot\rVert\colon V\to \mathbb{R}\) is called normed space.
Remarks
An ordered pair \((V,\lVert \cdot\rVert)\) of a vector space \(V\) over \(\mathbb{R}\) or \(\mathbb{C}\) and a norm \(\lVert \cdot\rVert\colon V\to \mathbb{R}\) is called normed space.