\begin{definition}[Definition:Convergent Mapping/Metric Space]
Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ be metric spaces.
Let $c$ be a limit point of $M_1$.
Let $f: A_1 \to A_2$ be a mapping from $A_1$ to $A_2$ defined everywhere on $A_1$ ''except possibly'' at $c$.
Let $\map f x$ tend to the limit $L$ as $x$ tends to $c$.
Then $f$ '''converges to the limit $L$ as $x$ tends to $c$'''.
\end{definition}