Spectral Spaces

Max Dickmann · Niels Schwartz · Marcus Tressl

maalis 2019 · New Mathematical Monographs Kirja 35 · Cambridge University Press

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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.

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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 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 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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