On the Gale-Nikaidô-Inada fundamental theorem on univalence of mappings (Q1920785)

The main result of the paper is the following theorem: For every integer \(n\geq 2\) there are an ellipsoid \(D\subset\mathbb{R}^n\) and a mapping \(F:D\to \mathbb{R}^n\) of class \(C^\infty\) such that each principal minor of the Jacobian matrix \(F'(x)\) is positive but \(F\) is not injective.