RT Journal Article
T1 Smooth surjections and surjective restrictions
A1 Aron, Richard M.
A1 Jaramillo Aguado, Jesús Ángel
A1 Le Donne, E.
AB 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.
PB Suomalainen tiedeakatemia
SN 1239-629X
YR 2017
FD 2017
LK https://hdl.handle.net/20.500.14352/18187
UL https://hdl.handle.net/20.500.14352/18187
LA eng
NO Ministerio de Economía y Competitividad (MINECO)
NO Academy of Finland
DS Docta Complutense
RD 11 may 2025