Timeline for Existence of a distinguished continuous version of the logarithm of a continuous function
Current License: CC BY-SA 4.0
3 events
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| Nov 15, 2020 at 16:16 | comment | added | Jochen Wengenroth | The compactness is heavily used in the proof that a continuous map which is homotopic to an inessential one is itself inessential: You need uniform continuity of the homotopy $f(t,x)$ to get $|f(t,x)-f(s,x)|$ small uniformly in $x\in E$ if $|s-t|$ is small enough. In the concrete case you would like to apply this with $f(t,x)=\varphi(tx)$ (or $\varphi(tx)/|\varphi(tx)|$) and hence, the global argument only seems to work under additional assumptions on $\varphi$. | |
| Nov 15, 2020 at 11:46 | comment | added | 0xbadf00d | Thank you for your answer. I'm actually aware of the proof you're describing. My main interest is really how the claim can be proved using the results of Dieudonneé. Do you've got any thoughts on that as well? | |
| Nov 15, 2020 at 11:34 | history | answered | Jochen Wengenroth | CC BY-SA 4.0 |