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.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 4$ A double induction principle and its applications: Definition $4.1$