Definition:Mapping Preserves Supremum/Join

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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 join if and only if

for every pair of elements $x, y$ of $S_1$, $f$ preserves the supremum of $\left\{ {x, y}\right\}$.


Sources