Definition:Distance/Points/Normed Vector Space

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

Let $x, y \in X$.

Then the function $\norm {\, \cdot \,} : X \times X \to \R$:
 * $\map d {x, y} = \norm {x - y}$

is called the distance between $x$ and $y$.