Aspects of power domains and power locales

Several equivalent approaches to power domains are presented: the naturality of this concept for denotational semantics is stressed and its modal interpretation is explained. We show how to solve equations involving power domains and apply the theory to an equation that leads to a characterization of bisimulations. Power locales are introduced, as the analogue of both power domains and power spaces. We study the monads defined by the power locales, their algebras and the points of the power locales