  In this paper, concepts of (topological) FS-approximation spaces are
introduced. Representations of FS-domains and BF-domains via (topological)
FS-approximation spaces are considered. It is proved that the collection of
CF-closed sets in an FS-approximation space (resp., a topological
FS-approximation space) endowed with the set-inclusion order is an FS-domain
(resp., a BF-domain) and that every FS-domain (resp., BF-domain) is order
isomorphic to the collection of CF-closed sets of some FS-approximation space
(resp., topological FS-approximation space) endowed with the set-inclusion
order. The concept of topological BF-approximation spaces is introduced and a
skillful method without using CF-approximable relations to represent BF-domains
is given. It is also proved that the category of FS-domains (resp., BF-domains)
with Scott continuous maps as morphisms is equivalent to that of
FS-approximation spaces (resp., topological FS-approximation spaces) with
CF-approximable relations as morphisms.
