Definition:Order-Reflecting Mapping

Definition
Let $\struct {S, \preceq_1}$ and $\struct {T, \preceq_2}$ be ordered sets.

Let $\phi: S \to T$ be a mapping.

Then $\phi$ is an order-reflecting mapping or reflects order :


 * $\forall x, y \in S: \map \phi x \preceq_2 \map \phi y \implies x \preceq_1 y$

Also see

 * Definition:Order-Preserving Mapping


 * Definition:Decreasing Mapping