Definition:Mapping Preserves Supremum/Finite
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Definition
Let $\left({S_1, \preceq_1}\right)$, $\left({S_2, \preceq_2}\right)$ be ordered sets.
Let $f: S_1 \to S_2$ be a mapping.
$f$ preserves finite suprema if and only if
- for every finite subset $F$ of $S_1$, $f$ preserves the supremum of $F$.