  Representations of domains mean in a general way representing a domain as a
suitable family endowed with set-inclusion order of some mathematical
structures. In this paper, representations of domains via CF-approximation
spaces are considered. Concepts of CF-approximation spaces and CF-closed sets
are introduced. It is proved that the family of CF-closed sets in a
CF-approximation space endowed with set-inclusion order is a continuous domain
and that every continuous domain is isomorphic to the family of CF-closed sets
of some CF-approximation space endowed with set-inclusion order. The concept of
CF-approximable relations is introduced using a categorical approach, which
later facilitates the proof that the category of CF-approximation spaces and
CF-approximable relations is equivalent to that of continuous domains and Scott
continuous maps.
