Polynomial images of \(\mathbb{R}^n\)
The authors make a step towards a characterization of polynomial images of a real affine space (which are always semialgebraic according to the Tarski-Seidenberg theorem). The main result is that the complements of finite sets and the open convex polyhedral cones, defined by independent linear forms, in real \(n\)-space are polynomial images of real \(n\)-spaces. For the proof, the authors find explicit polynomial maps realizing the required images. The paper presents several examples and open questions related to the topic.
scientific article; zbMATH DE number 1901783