2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221067We show that the Kuratowski imbedding of a Riemannian manifold in L^\infty, exploited in Gromov's proof of the systolic inequality for essential manifolds, admits an approximation by a (1+C)-bi-Lipschitz (onto its image), finite-dimensional imbedding for every C>0. Our key tool is the first variation formula thought of as a real statement in first-order logic, in the context of non-standard analysis.12 pages, 1 figureDifferential GeometryLogic53C23, 26E35text