Priestley Spaces, Quasi.hyperalgebraic Lattices and Smyth Powerdomains

We introduce the concept of quasi.hyperalgebraic lattice and prove that a complete lattice is a Priestley space with respect to the interval topology if and only if it is quasi.hyperalgebraic. Some characterizations of quasi.hyperalgebraic lattices are presented. We also prove that the Smyth powerdomain of a quasi.hyperalgebraic lattice is hyperalgebraic.