\begin{definition}[Definition:Restriction/Operation]
Let $\struct {S, \circ}$ be an algebraic structure.
Let $A, B \subseteq S$.
The '''restriction of $\circ$ to $A \times B$''' is denoted $\circ {\restriction_{A \times B} }$, and is defined as:
:$\forall a \in A, b \in B: a \mathbin {\circ {\restriction_{A \times B} } } b = a \circ b$
The notation $\circ {\restriction_{A \times B} }$ is generally used only if it is necessary to emphasise that $\circ {\restriction_{A \times B} }$ is strictly different from $\circ$ (through having a different domain).
When no confusion is likely to result, $\circ$ is generally used for both.
\end{definition}