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Spectral Spaces

$140.00 USD

Part of New Mathematical Monographs

  • Date Published: March 2019
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108609586

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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.

    • 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
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    Product details

    • Date Published: March 2019
    • format: Adobe eBook Reader
    • isbn: 9781108609586
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • 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.

  • Authors

    Max Dickmann, Centre National de la Recherche Scientifique (CNRS), Paris
    Max Dickmann has been a researcher at the Centre National de la Recherche Scientifique (CNRS), Paris, since 1974, Directeur de Recherche since 1988 and emeritus since 2007. His research interests include the applications of spectral spaces to real algebraic geometry, quadratic forms, and related topics.

    Niels Schwartz, Universität Passau, Germany
    Niels Schwartz is Professor of Mathematics at the Universität Passau, Germany, retired since 2016. Many of his publications are concerned with, or use, spectral spaces in essential ways. In particular, he has used spectral spaces to introduce the notion of real closed rings, an important topic in real algebra and geometry.

    Marcus Tressl, University of Manchester
    Marcus Tressl is a mathematician working in the School of Mathematics at the University of Manchester. His research interests include model theory, ordered algebraic structures, ring theory, differential algebra, and non-Hausdorff topology.

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