Definition:Closed under Mapping/Class Theory

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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.