\begin{definition}[Definition:Operation Induced by Restriction]
Let $\struct {S, \circ}$ be a magma.
Let $\struct {T, \circ} \subseteq \struct {S, \circ}$.
That is, let $T$ be a subset of $S$ such that $\circ$ is closed in $T$.
Then the restriction of $\circ$ to $T$, namely $\circ {\restriction_T}$, is called the '''(binary) operation induced on $T$ by $\circ$'''.
Note that this definition applies only if $\struct {T, \circ}$ is closed, by which virtue it is a submagma of $\struct {S, \circ}$.
\end{definition}