\begin{definition}[Definition:Differentiable Mapping/Real-Valued Function/Open Set]
Let $\mathbb X$ be an open subset of $\R^n$. 
Let $f: \mathbb X \to \R$ be a real-valued function.
Then $f$ is '''differentiable in the open set $\mathbb X$''' {{iff}} $f$ is differentiable at each point of $\mathbb X$.
\end{definition}