Aron, Richard M.Jaramillo Aguado, Jesús ÁngelLe Donne, E.2023-06-172023-06-1720171239-629X10.5186/aasfm.2017.4237https://hdl.handle.net/20.500.14352/18187Given a surjective mapping f : E -> F between Banach spaces, we investigate the existence of a subspace G of E, with the same density character as F, such that the restriction of f to G remains surjective. We obtain a positive answer whenever f is continuous and uniformly open. In the smooth case, we deduce a positive answer when f is a C-1-smooth surjection whose set of critical values is countable. Finally we show that, when f takes values in the Euclidean space R-n, in order to obtain this result it is not sufficient to assume that the set of critical values of f has zero-measure.engAtribución-NoComercial 3.0 Españahttps://creativecommons.org/licenses/by-nc/3.0/es/journal articlehttp://www.acadsci.fi/mathematica/Vol42/AronJaramilloLeDonne.htmlhttp://www.acadsci.fi/open access517.98515.1Smooth surjective mappingNonlinear quotientSurjective restrictionUniformly open mapDensity characterAnálisis funcional y teoría de operadoresTopología1210 Topología