Cover -- Half-title -- Series-title -- Title -- Copyright -- Contents -- Preface -- Acknowledgments -- Foreword to A Compendium of Continuous Lattices -- Introduction to A Compendium of Continuous Lattices -- Background and Plan of the Work -- Background and Motivation -- Plan of the Work -- O A Primer on Ordered Sets and Lattices -- O-1 Generalities and Notation -- Exercises -- Old notes -- O-2 Completeness Conditions for Lattices and Posets -- Exercises -- Old notes -- New notes -- O-3 Galois Connections -- Exercises -- Old notes -- O-4 Meet Continuous Lattices and Semilattices -- Exercises -- Old notes -- O-5 T Spaces and Order -- Exercises -- New notes -- I Order Theory of Domains -- I-1 The "Way-below" Relation -- The way-below relation and continuous posets -- Auxiliary relations -- Important examples -- Exercises -- Old notes -- New notes -- I-2 Products, Substructures and Quotients -- Products, projection, kernel and closure operators on domains -- Equational theory of continuous lattices -- Exercises -- Old notes -- New notes -- I-3 Irreducible Elements -- Open filters and irreducible elements -- Distributivity and prime elements -- Pseudoprime elements -- Exercises -- Old notes -- I-4 Algebraic Domains and Lattices -- Compact elements, algebraic and arithmetic domains -- Products, kernel and closure operators -- Completely irreducible elements -- Exercises -- Old notes -- New notes -- II The Scott Topology -- II-1 The Scott Topology -- Scott convergence -- The Scott topology of domains -- The Hofmann-Mislove Theorem -- Exercises -- Old notes -- New notes -- II-2 Scott-Continuous Functions -- Scott-continuous functions -- Function spaces and cartesian closed categories of dcpos -- FS-domains and bifinite domains -- Exercises -- Old notes -- New notes -- II-3 Injective Spaces -- Injective and densely injective spaces.

Monotone convergence spaces -- Exercises -- Old notes -- New notes -- II-4 Function Spaces -- The Isbell topology -- Spaces with a continuous topology -- On dcpos with a continuous Scott topology -- Exercises -- Old notes -- New notes -- III The Lawson Topology -- III-1 The Lawson Topology -- Exercises -- Old notes -- III-2 Meet Continuity Revisited -- Exercises -- Old notes -- New notes -- III-3 Quasicontinuity and Liminf Convergence -- Quasicontinuous domains -- The Lawson topology and liminf convergence -- Exercises -- Old notes -- New notes -- III-4 Bases and Weights -- Exercises -- Old notes -- New notes -- III-5 Compact Domains -- Exercises -- New notes -- IV Morphisms and Functors -- IV-1 Duality Theory -- Exercises -- Old notes -- IV-2 Duality of Domains -- Exercises -- New notes -- IV-3 Morphisms into Chains -- Exercises -- Old notes -- IV-4 Projective Limits -- Exercises -- Old notes -- IV-5 Pro-continuous and Locally Continuous Functors -- Exercises -- Old notes -- New notes -- IV-6 Fixed-Point Constructions for Functors -- Exercises -- New notes -- IV-7 Domain Equations and Recursive Data Types -- Domain equations for covariant functors -- Domain equations for mixed variance functors -- Examples of domain equations -- Exercises -- New notes -- IV-8 Powerdomains -- The Hoare powerdomain -- The Smyth powerdomain -- The Plotkin powerdomain -- Exercises -- New notes -- IV-9 The Extended Probabilistic Power Domain -- Exercises -- New notes -- V Spectral Theory of Continuous Lattices -- V-1 The Lemma -- Exercises -- Old notes -- V-2 Order Generation and Topological Generation -- Exercises -- Old notes -- V-3 Weak Irreducibles and Weakly Prime Elements -- Exercises -- Old notes -- V-4 Sober Spaces and Complete Lattices -- Exercises -- Old notes -- V-5 Duality for Distributive Continuous Lattices -- Exercises -- Old notes.

V-6 Domain Environments -- Exercises -- New notes -- VI Compact Posets and Semilattices -- VI-1 Pospaces and Topological Semilattices -- Exercises -- Old notes -- VI-2 Compact Topological Semilattices -- Exercises -- Old notes -- VI-3 The Fundamental Theorem of Compact Semilattices -- Exercises -- Old notes -- VI-4 Some Important Examples -- Old notes -- VI-5 Chains in Compact Pospaces and Semilattices -- Exercises -- Old notes -- VI-6 Stably Compact Spaces -- Exercises -- New notes -- VI-7 Spectral Theory for Stably Compact Spaces -- Exercises -- Old notes -- VII Topological Algebra and Lattice Theory: Applications -- VII-1 One-Sided Topological Semilattices -- Exercises -- Old notes -- VII-2 Topological Lattices -- Exercises -- Old notes -- New notes -- VII-3 Hypercontinuity and Quasicontinuity -- Exercises -- New notes -- VII-4 Lattices with Continuous Scott Topology -- Exercises -- Old notes -- Bibliography -- Books, Monographs, and Collections -- Conference Proceedings -- Articles -- Dissertations and Master's Theses -- Memos Circulated in the Seminar on Continuity in Semilattices (SCS) -- List of Symbols -- List of Categories -- Index.