Pointwise directed supremum
= Pointwise directed supremum
For a <directed set> of <Scott continuous maps> $f_i:D\to E$, its <least upper bound> is $f(x)=\sup_i f_i(x)$. The two directed suprema over $i$ and over inputs commute, proving that $f$ remains Scott continuous. Thus the <function space of complete partial orders> is a <complete partial order>.