Definition:Ordering on Mappings

Definition

Let $S$ be a set.

Let $\left({T, \preceq}\right)$ be an ordered set.

Let $f, g: S \to T$ be mappings.

Then ordering on mappings $f$ and $g$ denoted $f \preceq g$ is defined by

$\forall s \in S: f\left({s}\right) \preceq g\left({s}\right)$

Sources

• 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices

• Mizar article YELLOW_2:def 1