Definition. Upper bounds in the category \mathbf {Cpo} [dt-004R]

A cpo A is an upper bound of an \omega -chain of cpos in the category \mathbf {Cpo} if there is a family of continuous functions \{g_i : A_i \twoheadrightarrow A \mid i \in \mathbb {N}\} such that the following diagram commutes (i.e. g_i = g_{i+1} \circ f_i for all i \in \mathbb {N}):