Definition:Inclusion-Preserving Mapping

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Definition

Let $A$ and $B$ be sets.

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


Then $f$ is inclusion-preserving if and only if 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

Generalizations