A Positivstellensatz for rings of continuous functions
A one page proof (using the real spectrum) of the following result: Let \(f,g: X\to {\mathbb{R}}\) be a continuous functions on a topological space X, such that f is strictly positive on \(g^{-1}(0)\). Then there exist continuous functions u, v and w such that \((1+v^ 2)f=1+w^ 2+gu\).
scientific article; zbMATH DE number 4027634