Biblioteca de la Universidad Complutense de Madrid

Uniform approximation of continuous mappings by smooth mappings with no critical points on Hilbert manifolds

Impacto

Azagra Rueda, Daniel y Cepelledo Boiso, M.C. (2004) Uniform approximation of continuous mappings by smooth mappings with no critical points on Hilbert manifolds. Duke mathematical journal , 124 (1). pp. 47-66. ISSN 0012-7094

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Resumen

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.


Tipo de documento:Artículo
Palabras clave:Dimensional Banach-spaces; Morse-sard theorem; Singular maps; Image size; Negligibility; Sets
Materias:Ciencias > Matemáticas > Topología
Código ID:14775
Depositado:17 Abr 2012 11:55
Última Modificación:17 Abr 2012 11:55

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