Topological representations of Lawson compact algebraic L-domains and Scott domains

In this paper, the relationships between two important subclasses of algebraic dcpos and topological spaces which may not be \(\textrm{T}_0\) are discussed. The concepts of CFF-spaces and strong CFF-spaces are introduced by considering the properties of their topological bases. With these concepts, Lawson compact algebraic L-domains and Scott domains are successfully represented in purely topological terms. Moreover, equivalences of the categories corresponding to these two subclasses of algebraic dcpos are also provided. This opens a way of finding non-\(\textrm{T}_0\) topological characterizations for domains.