By Vladimir G. Berkovich
The aim of this booklet is to introduce a brand new proposal of analytic house over a non-Archimedean box. regardless of the entire disconnectedness of the floor box, those analytic areas have the standard topological homes of a posh analytic house, equivalent to neighborhood compactness and native arcwise connectedness. This makes it attainable to use the standard notions of homotopy and singular homology. The e-book incorporates a homotopic characterization of the analytic areas linked to convinced sessions of algebraic kinds and an interpretation of Bruhat-Tits constructions when it comes to those analytic areas. the writer additionally stories the relationship with the sooner idea of a inflexible analytic area. Geometrical issues are used to procure a few purposes, and the analytic areas are used to build the principles of a non-Archimedean spectral idea of bounded linear operators. This booklet calls for a heritage on the point of uncomplicated graduate classes in algebra and topology, in addition to a few familiarity with algebraic geometry. it might be of curiosity to analyze mathematicians and graduate scholars operating in algebraic geometry, quantity thought, and -adic research.
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