 Definition 2.8 (Continuous functions). If \({\langle D,\sqsubseteq _D \rangle},{\langle E,\sqsubseteq _E \rangle}\) are cpo’s and \(f : D \to E\) is monotonic, \(f\) is continuous if   \[f(\bigsqcup_i x_i) = \bigsqcup_i f(x_i)\]   for every increasing chain \(x_0 \sqsubseteq x_1 \sqsubseteq \ldots \subseteq D\).