Definition:Ordered Set of All Mappings

Definition
Let $L = \struct {S, \preceq}$ be an ordered set.

Let $X$ be a set.

The ordered set of all mappings from $X$ to $L$ is defined by:
 * $L^X := \struct {S^X, \precsim}$

where
 * $\forall f, g \in S^X: f \precsim g \iff f \preceq g$
 * $\preceq$ denotes the ordering on mappings,
 * $S^X$ denotes the set of all mappings from $X$ into $S$.

Also see

 * Ordered Set of All Mappings is Ordered Set