2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132508In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of these classic theorems are proved when we consider differenciable (not necessarily C^1) maps.9 pages, no figuresAlgebraic TopologyClassical Analysis and ODEs58C15: 47J07text