\begin{definition}[Definition:Continuous Mapping (Metric Space)/Space/Definition 1]
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 $A_2$.
$f$ is '''continuous from $\struct {A_1, d_1}$ to $\struct {A_2, d_2}$''' {{iff}} it is continuous at every point $x \in A_1$.
\end{definition}