2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126975Let N and P be smooth manifolds of dimensions n and p (n>=p>=2). Let Omega^{I}(N,P) denote an open subspace of J(N,P) which consists of all Boardman submanifolds Sigma^{J}(N,P) with J=< I in the lexicographic order. We will prove the homotopy principle in the existence level for Omega^{I}(N,P).The author added the description interpreting the homomorphism in (3.1) and revised several careless misprintsGeometric Topology58K30;57R45text