Classes of domains that are used in giving meaning to programming
language constructs have to be closed under such constructions as
Cartesian product and functions space.
In this talk we consider
($\omega$-)continuous domains coming with a quasi
metric or a measurement, respectively, the canonical topology of which
coincides with the Scott topology defined by the partial order and
show for some very general constructions how quasi metrics and
measurements, respectively, on the constructed set can be obtained
from those of the components in such a way that their canonical
topology coincides with the Scott topology again.
The constructions we
consider are dependent sum, dependent product and inverse limit of
$\omega$-chains.