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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 [1]
Ordered sets [1]
Examples from mathematics, computer science and social science [3]
Diagrams [7]
Maps between ordered sets [10]
The Duality Principle; down-sets and up-sets [12]
Maximal and minimal elements; top and bottom [15]
Building new ordered sets [17]
Exercises [21]
2. Lattices and complete lattices [27]
Lattices as ordered sets [27]
Complete lattices [33]
Chain conditions and completeness [37]
Completions [40]
Exercises [45]
3. CPOs, algebraic lattices and domains [50]
Directed joins and algebraic closure operators [51]
CPOs [54]
Finiteness, algebraic lattices and domains [58]
Information systems [63]
Exercises [79]
4. Fixpoint theorems [86]
Fixpoint theorems and their applications [86]
The existence of maximal elements and Zorn’s Lemma [99]
Exercises [103]
5. Lattices as algebraic structures [109]
Lattices as algebraic structures [109]
Sublattices, products and homomorphisms [111]
Congruences [114]
Exercises [123]
6. Modular and distributive lattices [130]
The M3-N5 Theorem [134]
Exercises [133]
7. Boolean algebras and their applications [143]
Boolean algebras [143]
Boolean terms and disjunctive normal form [146]
Meet LINDA: the Lindenbaum algebra [154]
Exercises [158]
8. Representation theory: the finite case [163]
The representation of finite Boolean algebras [163]
Join-irreducible elements [165]
The representation of finite distributive lattices [169]
Duality between finite distributive lattices and finite ordered sets [171]
Exercises [177]
9. Ideals and filters [184]
Ideals and filters [184]
Prime ideals, maximal ideals and ultrafilters [185]
The existence of prime ideals, maximal ideals and ultrafilters [187]
Exercises [190]
10. Representation theory: the general case [193]
Representation by lattices of sets [193]
The prime ideal space [195]
Duality [201]
Appendix: a topological toolkit [210]
Exercises [214]
11. Formal concept analysis [221]
Contexts and their concepts [221]
The fundamental theorem [223]
From theory to practice [227]
Exercises [231]
Notation index [241]
Index [243]```
Item type Home library Call number Materials specified Status Date due Barcode Course reserves
Libros
06 D248 (Browse shelf) Available A-6493

Bibliografía: p. [237]-240.

Preface vii --
1. Ordered sets [1] --
Ordered sets [1] --
Examples from mathematics, computer science and social science [3] --
Diagrams [7] --
Maps between ordered sets [10] --
The Duality Principle; down-sets and up-sets [12] --
Maximal and minimal elements; top and bottom [15] --
Building new ordered sets [17] --
Exercises [21] --
2. Lattices and complete lattices [27] --
Lattices as ordered sets [27] --
Complete lattices [33] --
Chain conditions and completeness [37] --
Completions [40] --
Exercises [45] --
3. CPOs, algebraic lattices and domains [50] --
Directed joins and algebraic closure operators [51] --
CPOs [54] --
Finiteness, algebraic lattices and domains [58] --
Information systems [63] --
Exercises [79] --
4. Fixpoint theorems [86] --
Fixpoint theorems and their applications [86] --
The existence of maximal elements and Zorn’s Lemma [99] --
Exercises [103] --
5. Lattices as algebraic structures [109] --
Lattices as algebraic structures [109] --
Sublattices, products and homomorphisms [111] --
Congruences [114] --
Exercises [123] --
6. Modular and distributive lattices [130] --
Lattices satisfying additional identities [130] --
The M3-N5 Theorem [134] --
Exercises [133] --
7. Boolean algebras and their applications [143] --
Boolean algebras [143] --
Boolean terms and disjunctive normal form [146] --
Meet LINDA: the Lindenbaum algebra [154] --
Exercises [158] --
8. Representation theory: the finite case [163] --
The representation of finite Boolean algebras [163] --
Join-irreducible elements [165] --
The representation of finite distributive lattices [169] --
Duality between finite distributive lattices and finite ordered sets [171] --
Exercises [177] --
9. Ideals and filters [184] --
Ideals and filters [184] --
Prime ideals, maximal ideals and ultrafilters [185] --
The existence of prime ideals, maximal ideals and ultrafilters [187] --
Exercises [190] --
10. Representation theory: the general case [193] --
Representation by lattices of sets [193] --
The prime ideal space [195] --
Duality [201] --
Appendix: a topological toolkit [210] --
Exercises [214] --
11. Formal concept analysis [221] --
Contexts and their concepts [221] --
The fundamental theorem [223] --
From theory to practice [227] --
Exercises [231] --
Notation index [241] --
Index [243] --

MR, 91h:06001

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