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Spectral Spaces: New Mathematical Monographs, cartea 35

Autor Max Dickmann, Niels Schwartz, Marcus Tressl
en Limba Engleză Hardback – 20 mar 2019
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.
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Specificații

ISBN-13: 9781107146723
ISBN-10: 1107146720
Pagini: 650
Dimensiuni: 160 x 235 x 40 mm
Greutate: 1.03 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria New Mathematical Monographs

Locul publicării:New York, United States

Cuprins

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.

Recenzii

'… 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
'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

Notă biografică


Descriere

Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.