### Impacto

### Downloads

Downloads per month over past year

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

Preview |
PDF
176kB | |

PDF
Restringido a Repository staff only 183kB |

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

## 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 |

### Origin of downloads

Repository Staff Only: item control page