Definition. Upper bounds in the category \mathbf {Cpo}^\mathbf {R} [dt-005G]
A cpo A is an upper bound of an \omega -chain of cpos A_i in the category \mathbf {Cpo}^\textbf {R} if there is a family of retraction pairs A_i \xtofrom [g_i]{f_i} A such that the following diagram commutes (i.e. for all i \in \mathbb {N}, (f_i, g_i) = (f_{i+1},g_{i+1}) \circ (s_i,t_i), where \circ is composition of retraction pairs):
