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This category contains definitions related to Restrictions.
Related results can be found in Category:Restrictions.

Let $f: S \to T$ be a mapping.

Let $X \subseteq S$.

Let $f \sqbrk X \subseteq Y \subseteq T$.

The restriction of $f$ to $X \times Y$ is the mapping $f {\restriction_{X \times Y} }: X \to Y$ defined as:

$f {\restriction_{X \times Y} } = f \cap \paren {X \times Y}$

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