Definition:Subset Relation on Mappings

Definition

Let $f$ and $g$ be mappings.

$f$ is a subset of $g$, denoted $f \subseteq g$, if and only if:

$\forall x \in \Dom f: \map f x = \map g x$

Also see

• Results about the subset relation can be found here.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $6$: Order Isomorphism and Transfinite Recursion: $\S 1$ A few preliminaries