The Resource Spectral spaces, Max Dickmann, Niels Schwartz, Marcus Tressl

Spectral spaces, Max Dickmann, Niels Schwartz, Marcus Tressl

Label
Spectral spaces
Title
Spectral spaces
Statement of responsibility
Max Dickmann, Niels Schwartz, Marcus Tressl
Creator
Contributor
Author
Subject
Language
eng
Summary
Spectral spaces are a class of topological spaces. They are a tool linking algebraic structures, in a very wide sense, with geometry. They were invented to give a functional representation of Boolean algebras and distributive lattices and subsequently gained great prominence as a consequence of Grothendieck's invention of schemes. There are more than 1,000 research articles about spectral spaces, but this is the first monograph. It provides an introduction to the subject and is a unified treatment of results scattered across the literature, filling in gaps and showing the connections between different results. The book includes new research going beyond the existing literature, answering questions that naturally arise from this comprehensive approach. The authors serve graduates by starting gently with the basics. For experts, they lead them to the frontiers of current research, making this book a valuable reference source
Member of
Cataloging source
NhCcYBP
http://library.link/vocab/creatorDate
1940-
http://library.link/vocab/creatorName
Dickmann, M. A.
Dewey number
514/.32
Index
no index present
LC call number
QA611.25
LC item number
.D53 2019
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorDate
  • 1950-
  • 1964-
http://library.link/vocab/relatedWorkOrContributorName
  • Schwartz, Niels
  • Tressl, Marcus
  • EBSCOhost
Series statement
New mathematical monographs
Series volume
35
http://library.link/vocab/subjectName
  • Topological spaces
  • Geometry, Algebraic
  • Commutative rings
Label
Spectral spaces, Max Dickmann, Niels Schwartz, Marcus Tressl
Link
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=2046178
Instantiates
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Cover; Half-title; Series information; Title page; Copyright information; Contents; Preface; An Outline of the History of Spectral Spaces; 1 Spectral Spaces and Spectral Maps; 1.1 The Definition of Spectral Spaces; 1.2 Spectral Maps and the Category of Spectral Spaces; 1.3 Boolean Spaces and the Constructible Topology; 1.4 The Inverse Topology; 1.5 Specialization and Priestley Spaces; 1.6 Examples; 1.7 Further Reading; 2 Basic Constructions; 2.1 Spectral Subspaces; 2.2 Products of Spectral Spaces; 2.3 Spectral Subspaces of Products; 2.4 Finite Coproducts; 2.5 Zariski, Real, and Other Spectra
  • 3 Stone Duality3.1 The Spectrum of a Bounded Distributive Lattice; 3.2 Stone Duality; 3.3 Spectral Spaces via Prime Ideals and Prime Filters; 3.4 The Boolean Envelope of a Bounded Distributive Lattice; 3.5 Inverse Spaces and Inverse Lattices; 3.6 The Spectrum of a Totally Ordered Set; 3.7 Further Reading; 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; 5 Properties of Spectral Maps
  • 5.1 Images of Proconstructible Sets under Spectral Maps5.2 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; 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 Identifying Maps; 6.5 Spectral Quotients and Lattices; 6.6 The Space of Connected Components; 7 Scott Topology and Coarse Lower Topology; 7.1 When Scott is Spectral
  • 7.2 Fine Coherent Posets and Complete Lattices7.3 The Coarse Lower Topology on Root Systems and Forests; 7.4 Finite and Infinite Words; 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; 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; 10 Colimits in Spec; 10.1 Coproducts; 10.2 Fiber Sums; 10.3 Colimits; 10.4 Constructions with Fiber Sums
  • 11 Relations of Spec with Other Categories11.1 The Spectral Reflection of a Topological Space; 11.2 The Sobrification; 11.3 Spectral Reflections of Continuous Maps; 11.4 Properties of Topological Spaces and their Spectral Reflections; 11.5 How Localic Spaces are Located in the Category of Spectral Spaces; 11.6 The Categories Spec and PoSets; 11.7 The Subcategory BoolSp of Spec; 12 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; 12.4 The Spectrum of a Noetherian Ring
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781316543870
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic reproduction.
Sound
unknown sound
Specific material designation
remote
System control number
(NhCcYBP)40029046222
Label
Spectral spaces, Max Dickmann, Niels Schwartz, Marcus Tressl
Link
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=2046178
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Cover; Half-title; Series information; Title page; Copyright information; Contents; Preface; An Outline of the History of Spectral Spaces; 1 Spectral Spaces and Spectral Maps; 1.1 The Definition of Spectral Spaces; 1.2 Spectral Maps and the Category of Spectral Spaces; 1.3 Boolean Spaces and the Constructible Topology; 1.4 The Inverse Topology; 1.5 Specialization and Priestley Spaces; 1.6 Examples; 1.7 Further Reading; 2 Basic Constructions; 2.1 Spectral Subspaces; 2.2 Products of Spectral Spaces; 2.3 Spectral Subspaces of Products; 2.4 Finite Coproducts; 2.5 Zariski, Real, and Other Spectra
  • 3 Stone Duality3.1 The Spectrum of a Bounded Distributive Lattice; 3.2 Stone Duality; 3.3 Spectral Spaces via Prime Ideals and Prime Filters; 3.4 The Boolean Envelope of a Bounded Distributive Lattice; 3.5 Inverse Spaces and Inverse Lattices; 3.6 The Spectrum of a Totally Ordered Set; 3.7 Further Reading; 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; 5 Properties of Spectral Maps
  • 5.1 Images of Proconstructible Sets under Spectral Maps5.2 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; 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 Identifying Maps; 6.5 Spectral Quotients and Lattices; 6.6 The Space of Connected Components; 7 Scott Topology and Coarse Lower Topology; 7.1 When Scott is Spectral
  • 7.2 Fine Coherent Posets and Complete Lattices7.3 The Coarse Lower Topology on Root Systems and Forests; 7.4 Finite and Infinite Words; 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; 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; 10 Colimits in Spec; 10.1 Coproducts; 10.2 Fiber Sums; 10.3 Colimits; 10.4 Constructions with Fiber Sums
  • 11 Relations of Spec with Other Categories11.1 The Spectral Reflection of a Topological Space; 11.2 The Sobrification; 11.3 Spectral Reflections of Continuous Maps; 11.4 Properties of Topological Spaces and their Spectral Reflections; 11.5 How Localic Spaces are Located in the Category of Spectral Spaces; 11.6 The Categories Spec and PoSets; 11.7 The Subcategory BoolSp of Spec; 12 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; 12.4 The Spectrum of a Noetherian Ring
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9781316543870
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic reproduction.
Sound
unknown sound
Specific material designation
remote
System control number
(NhCcYBP)40029046222

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