Category:Definitions/Increasing Mappings

This category contains definitions related to Increasing Mappings.
Related results can be found in Category:Increasing Mappings.

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

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

Then $\phi$ is increasing if and only if:

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

Note that this definition also holds if $S = T$.

Also see

• Category:Definitions/Decreasing Mappings