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## Introduction to lattices and order / B. A. Davey, H. A. Priestley.

Editor: Cambridge : Cambridge University Press, 1990Descripción: viii, 248 p. : il. ; 23 cmISBN: 0521367662 (pbk.); 0521365848Tema(s): Lattice theoryOtra clasificación: 06-01 (68Q55) Recursos en línea: Publisher description
Contenidos:
```Preface vii
1. Ordered sets 
Ordered sets 
Examples from mathematics, computer science and social science 
Diagrams 
Maps between ordered sets 
The Duality Principle; down-sets and up-sets 
Maximal and minimal elements; top and bottom 
Building new ordered sets 
Exercises 
2. Lattices and complete lattices 
Lattices as ordered sets 
Complete lattices 
Chain conditions and completeness 
Completions 
Exercises 
3. CPOs, algebraic lattices and domains 
Directed joins and algebraic closure operators 
CPOs 
Finiteness, algebraic lattices and domains 
Information systems 
Exercises 
4. Fixpoint theorems 
Fixpoint theorems and their applications 
The existence of maximal elements and Zorn’s Lemma 
Exercises 
5. Lattices as algebraic structures 
Lattices as algebraic structures 
Sublattices, products and homomorphisms 
Congruences 
Exercises 
6. Modular and distributive lattices 
The M3-N5 Theorem 
Exercises 
7. Boolean algebras and their applications 
Boolean algebras 
Boolean terms and disjunctive normal form 
Meet LINDA: the Lindenbaum algebra 
Exercises 
8. Representation theory: the finite case 
The representation of finite Boolean algebras 
Join-irreducible elements 
The representation of finite distributive lattices 
Duality between finite distributive lattices and finite ordered sets 
Exercises 
9. Ideals and filters 
Ideals and filters 
Prime ideals, maximal ideals and ultrafilters 
The existence of prime ideals, maximal ideals and ultrafilters 
Exercises 
10. Representation theory: the general case 
Representation by lattices of sets 
The prime ideal space 
Duality 
Appendix: a topological toolkit 
Exercises 
11. Formal concept analysis 
Contexts and their concepts 
The fundamental theorem 
From theory to practice 
Exercises 
Notation index 
Index ``` Average rating: 0.0 (0 votes)
Item type Home library Call number Materials specified Status Date due Barcode Course reserves Libros
06 D248 (Browse shelf) Available A-6493

Bibliografía: p. -240.

Preface vii --
1. Ordered sets  --
Ordered sets  --
Examples from mathematics, computer science and social science  --
Diagrams  --
Maps between ordered sets  --
The Duality Principle; down-sets and up-sets  --
Maximal and minimal elements; top and bottom  --
Building new ordered sets  --
Exercises  --
2. Lattices and complete lattices  --
Lattices as ordered sets  --
Complete lattices  --
Chain conditions and completeness  --
Completions  --
Exercises  --
3. CPOs, algebraic lattices and domains  --
Directed joins and algebraic closure operators  --
CPOs  --
Finiteness, algebraic lattices and domains  --
Information systems  --
Exercises  --
4. Fixpoint theorems  --
Fixpoint theorems and their applications  --
The existence of maximal elements and Zorn’s Lemma  --
Exercises  --
5. Lattices as algebraic structures  --
Lattices as algebraic structures  --
Sublattices, products and homomorphisms  --
Congruences  --
Exercises  --
6. Modular and distributive lattices  --
Lattices satisfying additional identities  --
The M3-N5 Theorem  --
Exercises  --
7. Boolean algebras and their applications  --
Boolean algebras  --
Boolean terms and disjunctive normal form  --
Meet LINDA: the Lindenbaum algebra  --
Exercises  --
8. Representation theory: the finite case  --
The representation of finite Boolean algebras  --
Join-irreducible elements  --
The representation of finite distributive lattices  --
Duality between finite distributive lattices and finite ordered sets  --
Exercises  --
9. Ideals and filters  --
Ideals and filters  --
Prime ideals, maximal ideals and ultrafilters  --
The existence of prime ideals, maximal ideals and ultrafilters  --
Exercises  --
10. Representation theory: the general case  --
Representation by lattices of sets  --
The prime ideal space  --
Duality  --
Appendix: a topological toolkit  --
Exercises  --
11. Formal concept analysis  --
Contexts and their concepts  --
The fundamental theorem  --
From theory to practice  --
Exercises  --
Notation index  --
Index  --

MR, 91h:06001

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