Artin-Lang property for analytic manifolds of dimension two
Let \(M\) be a two-dimensional paracompact real connected analytic manifold, let \({\mathcal O} (M)\) be the ring of analytic functions on \(M\) and let \(K\) be its quotient field. The author proves the so-called Artin-Lang property: Let \(f_1, \ldots, f_r \in {\mathcal O} (M)\). Then there is an ordering \(\beta\) in \(K\) in which they are simultaneously positive if and only if there exists a point \(x \in M\) such that \(f_1(x) > 0, \ldots, f_r(x) > 0\).
scientific article; zbMATH DE number 704934