# Definition:Relational Closure

## Definition

Let $A$ be a class.

Let $\RR \subseteq A \times A$ be a relation.

Let $x$ be a small class that is a subset of $A$.

The relational closure of $x$ is the smallest small class containing $x$ that is also $\RR$-transitive.

## Also see

• Results about relational closures can be found here.