This book contains articles on the notion of a continuous lattice, which has its roots in Dana Scott's work on a mathematical theory of computation, presented at a conference on categorical and topological aspects of continuous lattices held in 1982.
1. On the Topologies of Injective Spaces 2. Convergence and Continuity in Partially Ordered Sets and Semilattices 3. Natural Topologies, Essential Extensions, Reductive Lattices, and Congruence Extension 4. The Fell Compactification Revisited 5. The trace of the Weak Topology and of the Γ-Topology of Lop coincide on the Pseudo-Meet-Prime Elements of a Continuous Lattice L 6. Complete Distributivity and the Essential 7. Free Objects in the Category of Completely Distributive Lattices 8. Discontinuity of Meets and Joins 9. Vietoris Locales and Localic Semilattices 10. On the Exponential Law for Function Spaces Equipped with the Compact-Open Topology 11. The (Strong) Isbeil Topology and (Weakly) continuous Lattices 12. Obtaining the T0-Essential Hull 13. The Local Approach to Programming Language Theory 14. Algebraic Lattices as Dual Spaces of Distributive Lattices 15. Scott Topology, Isbeil Topology, and Continuous Convergence 16. Projectiveness with Regard to a Right Adjoint Functor 17. Lattices and Semilattices: A Convex Point of View