  In this paper, by means of upper approximation operators in rough set theory,
we study representations for sL-domains and its special subclasses. We
introduce the concepts of sL-approximation spaces, L-approximation spaces and
bc-approximation spaces, which are special types of CF-approximation spaces. We
prove that the collection of CF-closed sets in an sL-approximation space
(resp., an L-approximation space, a bc-approximation space) ordered by
set-theoretic inclusion is an sL-domain (resp., an L-domain, a bc-domain);
conversely, every sL-domain (resp., L-domain, bc-domain) is order-isomorphic to
the collection of CF-closed sets of an sL-approximation space (resp., an
L-approximation space, a bc-approximation space). Consequently, we establish an
equivalence between the category of sL-domains (resp., L-domains) with Scott
continuous mappings and that of sL-approximation spaces (resp., L-approximation
spaces) with CF-approximable relations.
