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 if and only if:

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

Also see

• Definition:Order-Preserving Mapping

• Definition:Decreasing Mapping

Sources

• 20 November 1998: Martín Hötzel Escardó: Properly injective spaces and function spaces (Topology and its Applications Vol. 89, no. 1–2: pp. 75 – 120)