Definition:Restriction/Operation

Definition
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.

Also see

 * Definition:Extension of Operation


 * Definition:Restriction of Relation
 * Definition:Restriction of Mapping


 * Definition:Operation Induced by Restriction