Definition:Ordering on Mappings
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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