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Smooth surjections and surjective restrictions

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Aron, Richard M. and Jaramillo Aguado, Jesús Ángel and Le Donne, E. (2017) Smooth surjections and surjective restrictions. Annales Academiæ Scientiarum Fennicae, 42 (2). pp. 525-534. ISSN 1239-629X

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Official URL: http://www.acadsci.fi/mathematica/Vol42/AronJaramilloLeDonne.html


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Smooth surjective mapping; Nonlinear quotient; Surjective restriction; Uniformly open map; Density character
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Topology
ID Code:45119
Deposited On:18 Oct 2017 09:42
Last Modified:23 Oct 2017 08:59

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