%0 Journal Article
%A Aron, Richard M.
%A Jaramillo Aguado, Jesús Ángel
%A Le Donne, E.
%T Smooth surjections and surjective restrictions
%D 2017
%@ 1239-629X
%U https://hdl.handle.net/20.500.14352/18187
%X Given 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.
%~