# Category:Restrictions

This category contains results about Restrictions.

Definitions specific to this category can be found in Definitions/Restrictions.

Let $\mathcal R$ be a relation on $S \times T$.

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

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

- $\mathcal R {\restriction_{X \times Y} }: = \mathcal R \cap \paren {X \times Y}$

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

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### E

## Pages in category "Restrictions"

The following 26 pages are in this category, out of 26 total.

### C

### R

- Restriction is Subset of Relation
- Restriction of Antireflexive Relation is Antireflexive
- Restriction of Antisymmetric Relation is Antisymmetric
- Restriction of Antitransitive Relation is Antitransitive
- Restriction of Asymmetric Relation is Asymmetric
- Restriction of Connected Relation is Connected
- Restriction of Inverse is Inverse of Restriction
- Restriction of Mapping is Mapping
- Restriction of Mapping to Image is Surjection
- Restriction of Non-Connected Relation is Not Necessarily Non-Connected
- Restriction of Non-Reflexive Relation is Not Necessarily Non-Reflexive
- Restriction of Non-Symmetric Relation is Not Necessarily Non-Symmetric
- Restriction of Non-Transitive Relation is Not Necessarily Non-Transitive
- Restriction of Reflexive Relation is Reflexive
- Restriction of Serial Relation is Not Necessarily Serial
- Restriction of Symmetric Relation is Symmetric
- Restriction of Transitive Relation is Transitive