Author | Gierz, Gerhard. author |
---|---|
Title | A Compendium of Continuous Lattices [electronic resource] / by Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel, Jimmie D. Lawson, Michael W. Mislove, Dana S. Scott |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1980 |
Connect to | http://dx.doi.org/10.1007/978-3-642-67678-9 |
Descript | XX, 371 p. online resource |
O. A Primer of Complete Lattices -- 1. Generalities and notation -- 2. Complete lattices -- 3. Galois connections -- 4. Meet-continuous lattices -- I. Lattice Theory of Continuous Lattices -- 1. The โway-belowโ relation -- 2. The equational characterization -- 3. Irreducible elements -- 4. Algebraic lattices -- II. Topology of Continuous Lattices: The Scott Topology -- 1. The Scott topology -- 2. Scott-continuous functions -- 3. Injective spaces -- 4. Function spaces -- III. Topology of Continuous Lattices: The Lawson Topology -- 1. The Lawson topology -- 2. Meet-continuous lattices revisited -- 3. Lim-inf convergence -- 4. Bases and weights -- IV. Morphisms and Functors -- 1. Duality theory -- 2. Morphisms into chains -- 3. Projective limits and functors which preserve them -- 4. Fixed point construction for functors -- V. Spectral Theory of Continuous Lattices -- 1. The Lemma -- 2. Order generation and topological generation -- 3. Weak irreducibles and weakly prime elements -- 4. Sober spaces and complete lattices -- 5. Duality for continuous Heyting algebras -- VI. Compact Posets and Semilattices -- 1. Pospaces and topological semilattices -- 2. Compact topological semilattices -- 3. The fundamental theorem of compact semilattices -- 4. Some important examples -- 5. Chains in compact pospaces and semilattices -- VII. Topological Algebra and Lattice Theory: Applications -- 1. One-sided topological semilattices -- 2. Topological lattices -- 3. Compact pospaces and continuous Heyting algebras -- 4. Lattices with continuous Scott topology -- Listof Symbols -- List of Categories