 Scott’s original model is built starting with a complete lattice \((D, \le)\). That is, \((D,\le)\) is a partially ordered set in which greatest lower bounds (infima) and least upper bounds (suprema) exist for arbitrary sets of elements. A function \(f\) from \((D,\le)\) into a complete lattice \((E,\le)\) is said to be continuous when it preserves the supremum of each ideal on \(D\), where an ideal is an upward directed downward closed subset.