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Artículo
Uniform approximation of continuous mappings by smooth mappings with no critical points on Hilbert manifolds
(Duke University Press, 2004-07-15)
We prove that every continuous mapping from a separable infinitedimensional Hilbert space X into R m can be uniformly approximated by C∞ smooth mappings with no critical points. This kind of result can be regarded as a ...
Artículo
Smooth Lipschitz retractions of starlike bodies onto their boundaries in infinite-dimensional Banach spaces
(London Mathematical Society, 2001)
Let X be an infinite-dimensional Banach space and let A be a Cp Lipschitz bounded starlike body (for instance the unit ball of a smooth norm). We prove that (1) The boundary ∂A is C p Lipschitz contractible. (2) There ...
Ponencia
Uniform approximation of continuous functions by smooth functions with no critical points on Hilbert manifolds
(2001)
We prove that every continuous function on a separable infinitedimensional Hilbert space X can be uniformly approximated by C∞ smooth functions with no critical points. This kind of result can be regarded as a sort of ...