2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99763Let n be any integer greater than two. We prove that there exists a projection P having the following properties. (1) P is not the projection of any unknotted knot. (2) The singular point set of P consists of double points. (3) P is the projection of an n-knot which is diffeomorphic to the standard sphere. We prove there exists an immersed n-sphere (in R^{n+1}\times{0}) which is not the projection of any n-knot (n>2). Note that the second theorem is different from the first one.12 pages, no figureGeometric TopologyMathematical Physics57M25, 57Q45text