Definition:Ordered Set of All Mappings

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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


Sources