  Robustness is a property of system analyses, namely monotonic maps from the
complete lattice of subsets of a (system's state) space to the two-point
lattice. The definition of robustness requires the space to be a metric space.
Robust analyses cannot discriminate between a subset of the metric space and
its closure, therefore one can restrict to the complete lattice of closed
subsets. When the metric space is compact, the complete lattice of closed
subsets ordered by reverse inclusion is w-continuous and robust analyses are
exactly the Scott continuous maps. Thus, one can also ask whether a robust
analysis is computable (with respect to a countable base). The main result of
this paper establishes a relation between robustness and Scott continuity, when
the metric space is not compact. The key idea is to replace the metric space
with a compact Hausdorff space, and relate robustness and Scott continuity by
an adjunction between the complete lattice of closed subsets of the metric
space and the w-continuous lattice of closed subsets of the compact Hausdorff
space. We demonstrate the applicability of this result with several examples
involving Banach spaces.
