The ultrafilter theorem in real algebraic geometry
This paper contains some variations on the theme of the ``ultrafilter theorem'' which gives a homeomorphism between the real spectrum of the coordinate ring of a real algebraic set V (with its constructible topology), and the Stone space of the boolean algebra of semialgebraic subsets of V. The first three sections fall under the rubric ``Stone duality'', as indicated by the author. He describes a general situation where prime filters of [subbasic\(| basic| constructible]\) [open\(| closed| void]\) subsets of a set Y coincide with points of Y (it is a pity that frequent errors concerning the notation for these nine families of subsets occur). This applies when Y is a subset of \(2^ A\) closed for the Tychonoff topology, for instance to the real spectrum of A which is considered in the fourth section. In this case, filters of open or closed basic subsets are related to subsets of the ring A, via abstract Stellensätze.
real spectrum of the coordinate ring of a real algebraic set
scientific article; zbMATH DE number 4177287