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Spectral Spaces (new Mathematical Monographs) 🔍
Max Dickmann, Niels Schwartz , Marcus Tressl Cambridge University Press (Virtual Publishing), New Mathematical Monographs (35), March 2019
英语 [en] · PDF · 6.1MB · 2019 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/zlib · Save
描述
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.
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
备用文件名
lgli/Spectral Spaces.pdf
备用文件名
lgrsnf/Spectral Spaces.pdf
备用文件名
zlib/Mathematics/Geometry and Topology/Max Dickmann, Niels Schwartz , Marcus Tressl/Spectral Spaces_4972561.pdf
备选作者
M. A. Dickmann; Niels Schwartz; Marcus Tressl
备用出版商
RCOG Press
备用版本
New mathematical monographs, 35, Cambridge, United Kingdom, 2019
备用版本
Cambridge University Press, Cambridge, United Kingdom, 2019
备用版本
United Kingdom and Ireland, United Kingdom
备用版本
New Mathematical Monographs (35), 1, 2019
元数据中的注释
0
元数据中的注释
lg2348632
元数据中的注释
{"edition":"1","isbns":["1107146720","1316543870","9781107146723","9781316543870"],"last_page":650,"publisher":"Cambridge University Press","series":"New Mathematical Monographs (35)"}
元数据中的注释
Referenced by: doi:10.1090/tran/7596 doi:10.4064/fm-31-1-103-134 doi:10.5802/afst.1275
备用描述
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
备用描述
This first monograph on spectral spaces will be useful for graduates and researchers in mathematics and theoretical computer science who want to connect algebra and logic with geometric concepts. It is a systematic introduction and at the same time a reference source that leads up to the frontiers of current research.
备用描述
Offers A Comprehensive Presentation Of Spectral Spaces Focussing On Their Topology And Close Connections With Algebra, Ordered Structures, And Logic.
开源日期
2019-04-08
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