2019/03/08 by Max Dickmann, Niels Schwartz, Marcus Tressl · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Rough Sets and Fuzzy Logic #Fuzzy and Soft Set Theory #Distributive property #Class (philosophy) #Subject (documents) #Computer science #Representation (politics) #Topological space #Mathematics #Algebra over a field #Pure mathematics #Artificial intelligence #Political science #World Wide Web
paper · doi:10.1017/9781316543870
openalex publication_date 2019/03/08 · openalex created_date 2022/02/13 · openalex updated_date 2026/07/30
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.