Category:Definitions/Restrictions
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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 $f {\restriction_X}$.
Pages in category "Definitions/Restrictions"
The following 22 pages are in this category, out of 22 total.
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- Definition:Restricted Mapping
- Definition:Restriction
- Definition:Restriction of Mapping
- Definition:Restriction of Operation
- Definition:Restriction of Ordering
- Definition:Restriction of Relation
- Definition:Restriction of Relation (Class Theory)
- Definition:Restriction/Mapping
- Definition:Restriction/Notation
- Definition:Restriction/Operation
- Definition:Restriction/Relation
- Definition:Restriction/Relation/Also known as
- Definition:Restriction/Relation/Class Theory
- Definition:Restriction/Technical Note