Can Pourciau's open mapping theorem be derived from Clarke's inverse mapping theorem easily?

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19520%2F21%3AA0000184" target="_blank" >RIV/47813059:19520/21:A0000184 - isvavai.cz</a>
Alternative codes found
RIV/67985840:_____/21:00537714
Result on the web
<a href="https://www.sciencedirect.com/science/article/abs/pii/S0022247X20310210" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0022247X20310210</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2020.124858" target="_blank" >10.1016/j.jmaa.2020.124858</a>

Result language
angličtina
Original language name
Can Pourciau's open mapping theorem be derived from Clarke's inverse mapping theorem easily?
Original language description
We discuss the possibility of deriving Pourciau's open mapping theorem from Clarke's inverse mapping theorem. We construct a Lipschitzian mapping g:ℝ³→ℝ² such that its Clarke generalized Jacobian ∂g(0) at the origin consists of 2×3 matrices of full rank, yet it is not possible to find a row vector such that the matrices augmented by the row vector are all of rank 3. Additionally, it is not possible to find any two-dimensional subspace 0∈W⊂ℝ³ such that the mapping W∋x↦Mx∈ℝ² is surjective for every matrix M∈∂g(0). We thus conclude that Pourciau’s open mapping theorem cannot be derived from Clarke’s inverse mapping theorem easily in general.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)