\begin{definition}[Definition:Lipschitz Continuity/Point]
Let $M = \left({A, d}\right)$ and $M' = \left({A', d\,'}\right)$ be metric spaces.
Let Let $f: A \to A'$ be a mapping.
Let $a\in A$.
$f$ is a '''Lipschitz continuous at $a$''' {{iff}} there exists a positive real number $K \in \R_{\ge 0}$ such that:
:$\forall x \in A: d\,' \left({f \left({x}\right), f \left({a}\right)}\right) \le K d \left({x, a}\right)$
\end{definition}