Inverse images of open sets under gradient mapping

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10408273" target="_blank" >RIV/00216208:11320/19:10408273 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pKFfa4ZG0S" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pKFfa4ZG0S</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10474-018-0885-9" target="_blank" >10.1007/s10474-018-0885-9</a>

Result language

angličtina

Original language name

Inverse images of open sets under gradient mapping

Original language description

For every pair of sets F,URd, d2, F being of Borel class F-sigma and U being nonempty, bounded and open, we construct a Frechet differentiable function f:RdR such that (delta f)-1(U) and the Hausdorff dimension of (delta f)-1(U)F does not exceed 1. Moreover (delta f)(Rd)U. This generalizes both Zeleny [10] and Deville-Matheron [8] results about the properties of open sets preimages under the gradient mapping.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Acta Mathematica Hungarica

ISSN

0236-5294

e-ISSN

—

Volume of the periodical

157

Issue of the periodical within the volume

2

Country of publishing house

HU - HUNGARY

Number of pages

16

Pages from-to

371-386

UT code for WoS article

000462823500007

EID of the result in the Scopus database

2-s2.0-85055720050