Spectral spaces:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, United Kingdom
Cambridge University Press
2019
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| Series: | New mathematical monographs
35 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, 633 Seiten Diagramme |
| ISBN: | 9781107146723 |
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MARC
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Record in the Search Index
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| adam_text | Contents Preface page ix An Outline of the History of Spectral Spaces 1 Spectral Spaces andSpectral Maps 1.1 1.2 1.3 1.4 1.5 1.6 1.7 2 3 The Definition of SpectralSpaces Spectral Maps and the Category of Spectral Spaces Boolean Spaces and the Constructible Topology The Inverse Topology Specialization and Priestley Spaces Examples Further Reading xiii 1 2 10 13 23 27 36 46 Basic Constructions 48 2.1 2.2 2.3 2.4 2.5 49 52 57 64 66 Spectral Subspaces Products of Spectral Spaces Spectral Subspaces of Products Finite Coproducts Zariski, Real, and Other Spectra Stone Duality 78 3.1 3.2 3.3 3.4 3.5 3.6 3.7 79 82 88 92 94 96 98 The Spectrum of a Bounded Distributive Lattice Stone Duality Spectral Spaces via Prime Ideals and PrimeFilters The Boolean Envelope of a Bounded Distributive Lattice Inverse Spaces and Inverse Lattices The Spectrum of a Totally Ordered Set Further Reading v
vi Contents 4 Subsets of Spectral Spaces 4.1 Quasi-Compact Subsets, Closure, and Generalization 4.2 Directed Subsets and Specialization Chains 4.3 Rank and Dimension 4.4 Minimal Points and Maximal Points 4.5 Convexity and Locally Closed Sets and Points 102 103 107 113 118 131 5 Properties of Spectral Maps 5.1 Images of Proconstructible Sets under Spectral Maps 5.2 Monomorphisms and Epimorphisms 5.3 Closed and Open Spectral Maps 5.4 Embeddings 5.5 Irreducible Maps and Dominant Maps 5.6 Extending Spectral Maps 141 142 145 151 156 163 165 6 Quotient Constructions 6.1 Spectral Quotients Modulo Relations 6.2 Saturated Relations 6.3 Spectral Orders and Spectral Relations 6.4 Quotients Modulo Equivalence Relations and Identify ing Maps 6.5 Spectral Quotients and Lattices 6.6 The Space of Connected Components 168 169 174 179 7 Scott Topology and Coarse Lower Topology 7.1 When Scott is Spectral 7.2 Fine Coherent Posets and Complete Lattices 7.3 The Coarse Lower Topology on Root Systems and Forests 7.4 Finite and Infinite Words 205 206 221 230 239 8 Special Classes of Spectral Spaces 8.1 Noetherian Spaces 8.2 Spectral Spaces with Scattered Patch Space 8.3 Heyting Spaces 8.4 Normal Spectral Spaces 8.5 Spectral Root Systems and Forests 246 247 261 267 279 290 9 Localic Spaces 9.1 Frames and Completeness 9.2 Localic Spaces ֊ Spectra of Frames 9.3 Localic Maps 9.4 Localic Subspaces 9.5 Localic Points 299 300 306 311 315 322 186 197 199
Contents 10 11 Colimits in Spec 328 10.1 10.2 Coproducts Fiber Sums 329 340 10.3 10.4 Colimits Constructions with Fiber Sums 354 360 Relations of Spec with Other Categories 369 11.1 The Spectral Reflection of a Topological Space 371 11.2 The Sobrification 384 11.3 Spectral Reflections of Continuous Maps 11.4 Properties of Topological Spaces and their Spectral Reflections 11.5 11.6 11.7 12 13 14 vii 390 393 How Localic Spaces are Located in the Category of Spectral Spaces 402 The Categories Spec and PoSets The Subcategory BoolSp of Spec 408 412 The Zariski Spectrum 12.1 The Zariski Spectrum - Topology on the Set of Prime Ideals of a Ring 12.2 Functoriality 12.3 Locally Closed Points and the Nullstellensatz 416 419 434 442 12.4 12.5 The Spectrum of a Noetherian Ring Zariski Spectra under Ring-Theoretic Constructions 450 458 12.6 Hochster’s Results 469 The Real Spectrum 485 13.1 Motivation and Elementary Examples 13.2 Specialization and Maximal Points 487 501 13.3 Spectral Morphisms Induced by Ring Homomorphisms 504 13.4 13.5 Real Spectra under Ring-Theoretic Constructions The Real Spectrum in Real Algebraic Geometry 515 518 13.6 Further Results and Reading 531 Spectral Spaces via Model Theory 540 14.1 The Model-Theoretic Setup 541 14.2 14.3 Spectral Spaces of Types Spectra of Structures and their Elementary Description 543 560
viii Contents Appendix: The Poset Zoo 579 References 590 Index of Categories and Functors 607 Index of Examples 608 Symbol Index 613 Subject Index 618
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| any_adam_object | 1 |
| author | Dickmann, Max 1940- Schwartz, Niels 1950- Tressl, Marcus 1964- |
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| discipline | Mathematik |
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| id | DE-604.BV045236881 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:12:24Z |
| institution | BVB |
| isbn | 9781107146723 |
| language | English |
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| physical | xvii, 633 Seiten Diagramme |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | New mathematical monographs |
| series2 | New mathematical monographs |
| spelling | Dickmann, Max 1940- Verfasser (DE-588)172054737 aut Spectral spaces Max Dickmann (Centre National de la Recherche Scientifique (CNRS), Paris France), Niels Schwartz (Universität Passau, Germany), Marcus Tressl (University of Manchester, UK) Cambridge, United Kingdom Cambridge University Press 2019 xvii, 633 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 35 Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 s Algebraische Geometrie (DE-588)4001161-6 s DE-604 Schwartz, Niels 1950- Verfasser (DE-588)1137734167 aut Tressl, Marcus 1964- Verfasser (DE-588)1184934126 aut Erscheint auch als Online-Ausgabe 9781316543870 New mathematical monographs 35 (DE-604)BV035420183 35 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030625152&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dickmann, Max 1940- Schwartz, Niels 1950- Tressl, Marcus 1964- Spectral spaces New mathematical monographs Algebraische Geometrie (DE-588)4001161-6 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4137586-5 |
| title | Spectral spaces |
| title_auth | Spectral spaces |
| title_exact_search | Spectral spaces |
| title_full | Spectral spaces Max Dickmann (Centre National de la Recherche Scientifique (CNRS), Paris France), Niels Schwartz (Universität Passau, Germany), Marcus Tressl (University of Manchester, UK) |
| title_fullStr | Spectral spaces Max Dickmann (Centre National de la Recherche Scientifique (CNRS), Paris France), Niels Schwartz (Universität Passau, Germany), Marcus Tressl (University of Manchester, UK) |
| title_full_unstemmed | Spectral spaces Max Dickmann (Centre National de la Recherche Scientifique (CNRS), Paris France), Niels Schwartz (Universität Passau, Germany), Marcus Tressl (University of Manchester, UK) |
| title_short | Spectral spaces |
| title_sort | spectral spaces |
| topic | Algebraische Geometrie (DE-588)4001161-6 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| topic_facet | Algebraische Geometrie Topologischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030625152&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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