# 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 $y$.