# Category:Restrictions

This category contains results about Restrictions.
Definitions specific to this category can be found in Definitions/Restrictions.

Let $\RR$ be a relation on $S \times T$.

Let $X \subseteq S$, $Y \subseteq T$.

The restriction of $\RR$ to $X \times Y$ is the relation on $X \times Y$ defined as:

$\RR {\restriction_{X \times Y} }: = \RR \cap \paren {X \times Y}$

Note that the parenthesis is not necessary in the above, but it does make the meaning clearer.

If $Y = T$, then we simply call this the restriction of $\RR$ to $X$, and denote it as $\RR {\restriction_X}$.