Real closed spaces
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).
scientific article; zbMATH DE number 3920650