# Definition:Relational Closure

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## Definition

Let $A$ be a class.

Let $\mathcal R \subseteq A \times A$ 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 $\mathcal R$-transitive.

## Also see

- Results about
**relational closures**can be found here.