Definition:Continuous Mapping (Normed Vector Space)/Space

Definition

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 $X_2$.

Definition 1

$f$ is continuous from $\struct{X_1, \norm {\,\cdot\,}_{X_1} }$ to $\struct{X_2, \norm {\,\cdot\,}_{X_2} }$ if and only if it is continuous at every point $x \in X_1$.