\begin{definition}[Definition:Continuous Extension/Real Function]
Let $A$, $B \subseteq \R$ be subsets of the real numbers such that $A \subseteq B$.
Let $f: A \to \R$ and $g: B \to \R$ be continuous real functions.
Then $g$ is a '''continuous extension''' of $f$ {{iff}}:
:$\forall x \in A : \map f x = \map g x$
Category:Definitions/Continuous Real Functions
\end{definition}