Function space of complete partial orders (source code)

= Function space of complete partial orders
{title2=$[D\to E]$}

The <Scott continuous maps> from $D$ to $E$, ordered pointwise. A nonempty directed family has pointwise supremum, and the constant-bottom function is least. Joint evaluation is Scott continuous: for a directed family of pairs $(f_i,x_i)$, directedness makes diagonal values cofinal among all $f_i(x_j)$. Evaluation and <currying> make the category of pointed complete partial orders and non-strict Scott continuous maps a <Cartesian closed category>.