Definition:Inclusion-Reversing Mapping
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Definition
Let $A, B$ be sets of sets and $\phi: A \to B$ be a mapping.
Then $\phi$ is inclusion-reversing if and only if:
- 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
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.