RT Journal Article
T1 Uniform approximation of continuous mappings by smooth mappings with no critical points on Hilbert manifolds
A1 Azagra Rueda, Daniel
A1 Cepelledo Boiso, M.C.
AB We prove that every continuous mapping from a separable infinite-dimensional Hilbert space X into R-m can be uniformly approximated by C-infinity-smooth mappings with no critical points. This kind of result can be regarded as a sort of strong approximate version of the Morse-Sard theorem. Some consequences of the main theorem are as follows. Every two disjoint closed subsets of X can be separated by a one-codimensional smooth manifold that is a level set of a smooth function with no critical points. In particular, every closed set in X can be uniformly approximated by open sets whose boundaries are C-infinity-smooth one-codimensional submanifolds of X. Finally, since every Hilbert manifold is diffeomorphic to an open subset of the Hilbert space, all of these results still hold if one replaces the Hilbert space X with any smooth manifold M modeled on X.
PB DUKE UNIV PRESS
SN 0012-7094
YR 2004
FD 2004
LK https://hdl.handle.net/20.500.14352/49823
UL https://hdl.handle.net/20.500.14352/49823
LA eng
NO Marie Curie Fellowship of the European Community Training and Mobility of
DS Docta Complutense
RD 8 may 2024