Continuous lattices and domains:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
93 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXXVI, 591 S. graph. Darst. |
| ISBN: | 0521803381 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804142776024039424 |
|---|---|
| adam_text | Titel: Continuous lattices and domains
Autor: Gierz, Gerhard
Jahr: 2003
Contents
Preface page xi
Acknowledgments xxi
Foreword to A Compendium of Continuous Lattices xxiii
Introduction to A Compendium of Continuous Lattices xxvii
O A Primer on Ordered Sets and Lattices 1
O-l Generalities and Notation 1
Exercises 7
Old notes 8
O-2 Completeness Conditions for Lattices and Posets 8
Exercises 17
Old notes 21
New notes 22
O-3 Galois Connections 22
Exercises 31
Old notes 35
O-4 Meet Continuous Lattices and Semilattices 36
Exercises 39
Old notes 41
O-5 7b Spaces and Order 41
Exercises 45
New notes 47
I Order Theory of Domains 48
1-1 The Way-below Relation 49
The way-below relation and continuous posets 49
Auxiliary relations 57
Important examples 62
vi Contents
Exercises 71
Old notes 75
New notes 78
1-2 Products, Substructures and Quotients 79
Products, projection, kernel and closure operators on
domains 79
Equational theory of continuous lattices 83
Exercises 90
Old notes 93
New notes 94
1-3 Irreducible elements 95
Open filters and irreducible elements 95
Distributivity and prime elements 98
Pseudoprime elements 106
Exercises 108
Old notes 114
1-4 Algebraic Domains and Lattices 115
Compact elements, algebraic and arithmetic domains 115
Products, kernel and closure operators 119
Completely irreducible elements 125
Exercises 127
Old notes 129
New notes 129
II The Scott Topology 131
II-1 The Scott Topology 132
Scott convergence 132
The Scott topology of domains 138
The Hofmann-Mislove Theorem 144
Exercises 151
Old notes 155
New notes 156
[1-2 Scott-Continuous Functions 157
Scott-continuous functions 157
Function spaces and cartesian closed categories of
dcpos 161
FS-domains and bifinite domains 165
Exercises 171
Old notes 176
New notes 176
Contents vii
II-3 injective Spaces 176
Injective and densely injective spaces 177
Monotone convergence spaces 182
Exercises 185
Old notes 187
New notes 187
II-4 Function Spaces 187
The Isbell topology 187
Spaces with a continuous topology 190
On dcpos with a continuous Scott topology 197
Exercises 204
Old notes 206
New notes 207
III The Lawson Topology 208
III-1 The Lawson Topology 209
Exercises 216
Old notes 218
III-2 Meet Continuity Revisited 219
Exercises 224
Old notes 225
New notes 226
III-3 Quasicontinuity and Liminf Convergence 226
Quasicontinuous domains 226
The Lawson topology and Liminf convergence 231
Exercises 236
Old notes 240
New notes 240
III-4 Bases and Weights 240
Exercises 249
Old notes 252
New notes 252
III-5 Compact Domains 253
Exercises 261
New notes 263
IV Morphisms and Functors 264
IV-1 Duality Theory 266
Exercises 279
Old notes 279
viii Contents
IV-2 Duality of Domains 280
Exercises 289
New notes 290
IV-3 Morphisms into Chains 290
Exercises 301
Old notes 304
IV-4 Projective Limits 305
Exercises 317
Old notes 317
IV-5 Pro-continuous and Locally Continuous
Functors 318
Exercises 329
Old notes 330
New notes 330
IV-6 Fixed-Point Constructions for Functors 330
Exercises 340
New notes 342
IV-7 Domain Equations and Recursive Data Types 343
Domain equations for covariant functors 344
Domain equations for mixed variance functors 351
Examples of domain equations 355
Exercises 357
New notes 358
IV-8 Powerdomains 359
The Hoare powerdomain 361
The Smyth powerdomain 363
The Plotkin powerdomain 364
Exercises 372
New notes 374
IV-9 The Extended Probabilistic Powerdomain 374
Exercises 391
New notes 392
V Spectral Theory of Continuous Lattices 394
V-l The Lemma 395
Exercises 399
Old notes 399
V-2 Order Generation and Topological Generation 400
Exercises 402
Old notes 403
Contents
V-3 Weak Irreducibles and Weakly Prune Elements 403
Exercises 406
Old notes 407
V-4 Sober Spaces and Complete Lattices 408
Exercises 414
Old notes 415
V-5 Duality for Distributive Continuous Lattices 415
Exercises 423
Old notes 429
V-6 Domain Environments 431
Exercises 437
New notes 437
VI Compact Posets and Semilattices 439
VI-1 Pospaces and Topological Semilattices 440
Exercises 444
Old notes 445
VI-2 Compact Topological Semilattices 445
Exercises 449
Old notes 450
VI-3 The Fundamental Theorem of Compact
Semilattices 450
Exercises 457
Old notes 462
VI-4 Some Important Examples 462
Old notes 467
VI-5 Chains in Compact Pospaces and Semilattices 468
Exercises 472
Old notes 473
VI-6 Stably Compact Spaces 474
Exercises 484
New notes 486
VI-7 Spectral Theory for Stably Compact Spaces 486
Exercises 489
Old notes 491
VII Topological Algebra and Lattice Theory: Applications 492
VII-1 One-Sided Topological Semilattices 493
Exercises 498
Old notes 499
Contents
VII-2 Topological Lattices 499
Exercises 504
Old notes 507
New notes 508
VII-3 Hypercontinuity and Quasicontinuity 508
Exercises 515
New notes 515
VII-4 Lattices with Continuous Scott Topology 515
Exercises 521
Old notes 522
Bibliography 523
Books, Monographs, and Collections 523
Conference Proceedings 526
Articles 528
Dissertations and Master s Theses 559
Memos Circulated in the Seminar on Continuity in
Semilattices (SCS) 564
List of Symbols 568
List of Categories 572
Index 575
|
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| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV025594039 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:37:08Z |
| institution | BVB |
| isbn | 0521803381 |
| language | English |
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| physical | XXXVI, 591 S. graph. Darst. |
| publishDate | 2003 |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Continuous lattices and domains G. Gierz ... 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2003 XXXVI, 591 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 93 Vollständiger Verband (DE-588)4425949-9 gnd rswk-swf Verband Mathematik (DE-588)4062565-5 gnd rswk-swf Vollständiger Verband (DE-588)4425949-9 s DE-604 Verband Mathematik (DE-588)4062565-5 s Gierz, Gerhard Sonstige oth Encyclopedia of mathematics and its applications 93 (DE-604)BV000903719 93 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020190182&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Continuous lattices and domains Encyclopedia of mathematics and its applications Vollständiger Verband (DE-588)4425949-9 gnd Verband Mathematik (DE-588)4062565-5 gnd |
| subject_GND | (DE-588)4425949-9 (DE-588)4062565-5 |
| title | Continuous lattices and domains |
| title_auth | Continuous lattices and domains |
| title_exact_search | Continuous lattices and domains |
| title_full | Continuous lattices and domains G. Gierz ... |
| title_fullStr | Continuous lattices and domains G. Gierz ... |
| title_full_unstemmed | Continuous lattices and domains G. Gierz ... |
| title_short | Continuous lattices and domains |
| title_sort | continuous lattices and domains |
| topic | Vollständiger Verband (DE-588)4425949-9 gnd Verband Mathematik (DE-588)4062565-5 gnd |
| topic_facet | Vollständiger Verband Verband Mathematik |
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