[Settfa] [Set Theory]Tuesday 14 May, Marián Fabian

[Wieslaw Kubis]

Dear all,

There is a small (yet mathematically important) correction in the 
abstract below, namely, an involution should be continuous (marked in 
capitals below).

Best wishes,

Wieslaw


Dne 11. 05. 24 v 9:00 kubis at math.cas.cz napsal(a):
> Set Theory and Analysis
>
> Tuesday 14 May 2024 - 10:00 to 11:30
> Place: IM, konírna
>
> Speaker: Marián Fabian, IM CAS
> Title: Fréchet differentiability versus Gateaux differentiability - 
> counter-examples
>
> Abstract
>
> We investigate several statements from analysis, what happens if 
> Fréchet differentiability
>
> is replaced by Gateaux differentiability. A culminating result is an 
> example showing non-validity of
>
> ``Gateaux'' form of chain rule: There exists a CONTINUOUS involution 
> $f:\R^^2 \longrightarrow \R^^2 $, Gateaux differentiable at (0,0), 
> with singular Jacobian Jf(0,0)=( 0 0 // 1 0), and hence
>
> Jf(0,0) Jf(0,0) = (0 0 // 0 0), which is not identity matrix.
>
>
> The statements presented come from a forthcoming joint paper of Jan 
> Kolar and me.
>
> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/6
>
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