Definition:Inclusion-Preserving Mapping

Definition
Let $A$ and $B$ be sets.

Let $f : A \to B$ be a mapping.

Then $f$ is inclusion-preserving for every two sets $a_1, a_2 \in A$:
 * $a_1 \subseteq a_2 \implies f(a_1) \subseteq f(a_2)$

Also see

 * Definition:Inclusion-Reversing Mapping

Generalizations

 * Definition:Increasing Mapping