Real closed spaces
type: Item
instance of: scholarly article
title: Real closed spaces
zbMATH Open document ID: 0576.14023
DOI: 10.1216/RMJ-1984-14-4-971
author: Niels Schwartz
published in: Rocky Mountain Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: In order to extend the theory of semi-algebraic spaces [see \textit{H. Delfs} and \textit{M. Knebusch}, ''Locally semialgebraic spaces'', Lect. Notes Math. 1173 (1985)] in the same way as schemes extend the classical theory of varieties a sheaf of rings is introduced on any constructible subset of the real spectrum [see \textit{M. Coste} and \textit{M.-F. Roy}, Contemp. Math. 8, 27-59 (1982; Zbl 0485.14007)] of a ring. This construction leads to affine-real closed spaces. Arbitrary real closed spaces are obtained by gluing affine pieces together along open subspaces. The real closed spaces form a category in which one can work very much as in the category of schemes. This is an abstract of the authors Habilitationsschrift ''Real closed spaces'' (München 1984).
Mathematics Subject Classification ID: 14Pxx
Mathematics Subject Classification ID: 14A15
Mathematics Subject Classification ID: 12D15
zbMATH DE Number: 3920650
zbMATH Keywords: semi-algebraic spaces
zbMATH Keywords: real spectrum
zbMATH Keywords: affine-real closed spaces
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3920650