\begin{definition}[Definition:Continuity/Functional]
Let $S$ be a set of mappings.
Let $y \in S$ be a mapping.
Let $J \sqbrk y: S \to \R$ be a functional.
Suppose:
  
:$\forall \epsilon \in \R_{>0}: \exists \delta \in \R_{>0}: \size {y - y_0} < \delta \implies \size {J \sqbrk y - J \sqbrk {y_0} } < \epsilon$
Then $J \sqbrk y$ is said to be a '''continuous functional''' and is continuous at the point $y_0 \in S$.
\end{definition}