Definition:Lipschitz Continuity/Point

Definition
Let $M = \struct {A, d}$ and $M' = \struct {A', d'}$ be metric spaces.

Let Let $f: A \to A'$ be a mapping. Let $a \in A$.

$f$ is a Lipschitz continuous at $a$ there exists a positive real number $K \in \R_{\ge 0}$ such that:
 * $\forall x \in A: \map {d'} {\map f x, \map f a} \le K \map d {x, a}$