Definition. Information ordering in $\textbf {Cpo}^\textbf {R}$ [dt-0059]

The third point in Corollary [dt-0057] suggests a notion of approximation, or information ordering, for cpos. Rather than say, as we did in § [dt-004O], that for cpos $A$ and $B$ , $A \sqsubseteq B$ iff there exists a continuous function $A\twoheadrightarrow B$ , we now say:

A \sqsubseteq B

iff there exists a retraction pair

A \xtofrom [g]{f} B


( $y \mapsto b \mapsto z$ but $z \not \sqsubseteq y$ )	( $b \mapsto x \mapsto a$ but $a \neq b$ )