\begin{definition}[Definition:Continuous Mapping (Normed Vector Space)/Space/Definition 1]
Let $M_1 = \struct{X_1, \norm {\,\cdot\,}_{X_1}}$ and $M_2 = \struct{X_2, \norm {\,\cdot\,}_{X_2}}$ be normed vector spaces.
Let $f: X_1 \to X_2$ be a mapping from $X_1$ to $X_2$.
$f$ is '''continuous from $\struct{X_1, \norm {\,\cdot\,}_{X_1} }$ to $\struct{X_2, \norm {\,\cdot\,}_{X_2} }$''' {{iff}} it is continuous at every point $x \in X_1$.
\end{definition}