Spectral Spaces
£155.00
Part of New Mathematical Monographs
- Authors:
- Max Dickmann, Centre National de la Recherche Scientifique (CNRS), Paris
- Niels Schwartz, Universität Passau, Germany
- Marcus Tressl, University of Manchester
- Date Published: March 2019
- availability: Available
- format: Hardback
- isbn: 9781107146723
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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.
Read more- Presents many applications of spectral spaces, their benefits, and how they naturally arise in different contexts
- Contains a large number of examples and counterexamples to help the reader learn the material
- Comprehensive indexes make the book a useful reference resource
Reviews & endorsements
'… this book is a valuable resource for anyone seriously interested in the theory of spectral spaces and represents a substantial addition to the literature on the subject.' Jimmie Lawson, New Mathematical Monographs
See more reviews'The book covers a substantial amount of material that had not been considered before. It also contains material available nowhere else in book form.' Tomasz Kubiak, Mathematical Reviews Clippings
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×Product details
- Date Published: March 2019
- format: Hardback
- isbn: 9781107146723
- length: 650 pages
- dimensions: 235 x 160 x 40 mm
- weight: 1.04kg
- availability: Available
Table of Contents
Outline of the history of spectral spaces
1. Spectral spaces and spectral maps
2. Basic constructions
3. Stone duality
4. Subsets of spectral spaces
5. Properties of spectral maps
6. Quotient constructions
7. Scott topology and coarse lower topology
8. Special classes of spectral spaces
9. Localic spaces
10. Colimits in Spec
11. Relations of Spec with other categories
12. The Zariski spectrum
13. The real spectrum
14. Spectral spaces via model theory
Appendix. The poset zoo
References
Index of categories and functors
Index of examples
Symbol index
Subject index.
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