Given an \omega -chain:
The colimit (or inverse limit) is the cpo of \omega -tuples:
D_\infty \; \triangleq \; \left \{ (x_0, x_1, \dots ) \mid x_i \in D_i \land x_i = g_i(x_{i+1}) \right \}
That is, it is countable sequence of elements, one for each domain D_i, where each element is consistent with earlier elements.
Ordering: The ordering is the pointwise ordering of products, naturally generalised to \omega -tuples. Under this ordering, D_\infty is a cpo. In fact if each D_i is a Scott domain, so is D_\infty .
