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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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