# Definition:Closed under Mapping/Class Theory

## Definition

Let $A$ and $B$ be classes such that $A$ is a subclass of $B$.

Let $g: B \to B$ be a mapping on $B$.

Then $A$ is closed under $g$ if and only if:

$\forall x \in A: \map g x \in A$

## Also see

• Results about closedness under mappings can be found here.