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 descriptionPreface 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] Appendix: further reading [237] Notation index [241] Index [243]
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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] --
Appendix: further reading [237] --
Notation index [241] --
Index [243] --
MR, 91h:06001
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