Definition:Reflexive Closure/Intersection of Reflexive Supersets

Definition

Let $\RR$ be a relation on a set $S$.

Let $\QQ$ be the set of all reflexive relations on $S$ that contain $\RR$.

The reflexive closure of $\RR$ is denoted $\RR^=$, and is defined as:

$\RR^= := \bigcap \QQ$

That is:

$\RR^=$ is the intersection of all reflexive relations on $S$ containing $\RR$.

Also see

• Equivalence of Definitions of Reflexive Closure

• Results about reflexive closures can be found here.