Definition:Inclusion-Reversing Mapping

Definition
Let $A, B$ be sets of sets and $\phi: A \to B$ be a mapping.

Then $\phi$ is inclusion-reversing :
 * for every pair of sets $a_1, a_2 \in A$ such that $a_1 \subseteq a_2$:
 * $\map \phi {a_2} \subseteq \map \phi {a_1}$

Also see

 * Definition:Inclusion-Preserving Mapping

Generalizations

 * When $\struct {A, \subseteq}$ and $\struct {B, \subseteq}$ are sets ordered by the subset relation, an inclusion-reversing mapping can be referred to as a decreasing mapping.


 * Definition:Contravariant Functor