Definition:Order-Reflecting Mapping

Definition
Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be ordered sets.

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

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


 * For all $x, y \in S: \left({ \phi\left({x }\right) \preceq_2 \phi\left({y}\right) \implies x \preceq_1 y }\right)$

Also see
Definition:Order-Preserving Mapping