Introduction to lattices and order:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2002
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 298 S. graph. Darst. |
| ISBN: | 0521784514 9780521784511 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to lattices and order |c B. A. Davey ; H. A. Priestley |
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Record in the Search Index
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| adam_text |
Titel: Introduction to lattices and order
Autor: Davey, Brian A
Jahr: 2002
Contents
Preface to the second edition viii
Preface to the first edition x
1. Ordered sets 1
Ordered sets 1
Examples from social science and Computer science 5
Diagrams: the art of drawing ordered sets 10
Constructing and de-constructing ordered sets 14
Down-sets and up-sets 20
Maps between ordered sets 23
Exercises 25
2. Lattices and complete lattices 33
Lattices as ordered sets 33
Lattices as algebraic structures 39
Sublattices, products and homomorphisms 41
Ideals and filters 44
Complete lattices and p|~structures 46
Chain conditions and completeness 50
Join-irreducible elements 53
Exercises 56
3. Formal concept analysis 65
Contexts and their concepts 65
The fundamental theorem of concept lattices 70
From theory to practice 74
Exercises 79
4. Modular, distributive and Boolean lattices 85
Lattices satisfying additional identities 85
The M3-N5 Theorem 88
Boolean lattices and Boolean algebras 93
Boolean terms and disjunctive normal form 96
Exercises 104
vi Contents
5. Representation: the finite case 112
Building blocks for lattices 112
Finite Boolean algebras are powerset algebras 114
Finite distributive lattices are down-set lattices 116
Finite distributive lattices and finite ordered sets in
partnership 119
Exercises 124
6. Congruences 130
Introducing congruences 130
Congruences and diagrams 134
The lattice of congruences of a lattice 137
Exercises 140
7. Complete lattices and Galois connections 145
Closure Operators 145
Complete lattices Coming from algebra: algebraic lattices 148
Galois connections 155
Completions 165
Exercises 169
8. CPOs and fixpoint theorems 175
CPOs 175
CPOs of partial maps 180
Fixpoint theorems 182
Calculating with fixpoints 189
Exercises 193
9. Domains and Information Systems 201
Domains for Computing 201
Domains re-modelled: Information Systems 204
Using fixpoint theorems to solve domain equations 221
Exercises 223
10. Maximality principles 228
Do maximal elements exist? - Zorn's Lemma and the
Axiom of Choice 228
Prime and maximal ideals 232
Powerset algebras and down-set lattices revisited 237
Contents vii
Exercises 244
11. Representation: the general case 247
Stone's representation theorem for Boolean algebras 247
Meet LINDA: the Lindenbaum algebra 252
Priestley's representation theorem for distributive lattices 256
Distributive lattices and Priestley Spaces in partnership 261
Exercises 267
Appendix A: a topological toolkit 275
Appendix B: further reading 280
Notation index 286
Index 289 |
| any_adam_object | 1 |
| author | Davey, Brian A. Priestley, Hilary A. |
| author_facet | Davey, Brian A. Priestley, Hilary A. |
| author_role | aut aut |
| author_sort | Davey, Brian A. |
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| building | Verbundindex |
| bvnumber | BV013187322 |
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| classification_tum | MAT 065f MAT 060f |
| ctrlnum | (OCoLC)248201554 (DE-599)BVBBV013187322 |
| dewey-full | 511.33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.33 |
| dewey-search | 511.33 |
| dewey-sort | 3511.33 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV013187322 |
| illustrated | Illustrated |
| indexdate | 2025-03-18T15:01:28Z |
| institution | BVB |
| isbn | 0521784514 9780521784511 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008986140 |
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| publishDate | 2002 |
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| publisher | Cambridge Univ. Press |
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| spelling | Davey, Brian A. Verfasser aut Introduction to lattices and order B. A. Davey ; H. A. Priestley 2. ed. Cambridge [u.a.] Cambridge Univ. Press 2002 XII, 298 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Geordnete Menge Gitter <Mathematik> Verbandstheorie Gitter Mathematik (DE-588)4157375-4 gnd rswk-swf Verband Mathematik (DE-588)4062565-5 gnd rswk-swf Geordnete Menge (DE-588)4156748-1 gnd rswk-swf Verbandstheorie (DE-588)4127072-1 gnd rswk-swf Gitter Mathematik (DE-588)4157375-4 s DE-604 Verbandstheorie (DE-588)4127072-1 s Geordnete Menge (DE-588)4156748-1 s Verband Mathematik (DE-588)4062565-5 s 1\p DE-604 Priestley, Hilary A. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008986140&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Davey, Brian A. Priestley, Hilary A. Introduction to lattices and order Geordnete Menge Gitter <Mathematik> Verbandstheorie Gitter Mathematik (DE-588)4157375-4 gnd Verband Mathematik (DE-588)4062565-5 gnd Geordnete Menge (DE-588)4156748-1 gnd Verbandstheorie (DE-588)4127072-1 gnd |
| subject_GND | (DE-588)4157375-4 (DE-588)4062565-5 (DE-588)4156748-1 (DE-588)4127072-1 |
| title | Introduction to lattices and order |
| title_auth | Introduction to lattices and order |
| title_exact_search | Introduction to lattices and order |
| title_full | Introduction to lattices and order B. A. Davey ; H. A. Priestley |
| title_fullStr | Introduction to lattices and order B. A. Davey ; H. A. Priestley |
| title_full_unstemmed | Introduction to lattices and order B. A. Davey ; H. A. Priestley |
| title_short | Introduction to lattices and order |
| title_sort | introduction to lattices and order |
| topic | Geordnete Menge Gitter <Mathematik> Verbandstheorie Gitter Mathematik (DE-588)4157375-4 gnd Verband Mathematik (DE-588)4062565-5 gnd Geordnete Menge (DE-588)4156748-1 gnd Verbandstheorie (DE-588)4127072-1 gnd |
| topic_facet | Geordnete Menge Gitter <Mathematik> Verbandstheorie Gitter Mathematik Verband Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008986140&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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