\begin{definition}[Definition:Continuous Mapping (Metric Space)/Point/Definition 4]
Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ be metric spaces.
Let $f: A_1 \to A_2$ be a mapping from $A_1$ to $A_2$.
Let $a \in A_1$ be a point in $A_1$.
$f$ is '''continuous at (the point) $a$ (with respect to the metrics $d_1$ and $d_2$)''' {{iff}}:
:for each neighborhood $N'$ of $\map f a$ in $M_2$ there exists a corresponding neighborhood $N$ of $a$ in $M_1$ such that $f \sqbrk N \subseteq N'$.
\end{definition}