2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62813We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation betwen them is described. A tangent structure is constructed for each pre-convenient space. This one is proved to be convenient iff the space and the tangent fibres coincide. Some basic comments on the relation with manifolds are given.2 files, 15 pages totalDifferential Geometrytext