Timeline for Functions that map open balls to open balls of different radius?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 7, 2019 at 11:12 | history | edited | Martin Kell | CC BY-SA 4.0 |
added 1 character in body
|
| Jan 7, 2019 at 11:11 | comment | added | Martin Kell | Seems i should avoid doing math at Sunday night. The projection is indeed not necessarily a balloon map. So the proof is still incomplete. | |
| Jan 7, 2019 at 11:05 | history | edited | Martin Kell | CC BY-SA 4.0 |
deleted 1208 characters in body
|
| Jan 7, 2019 at 0:19 | comment | added | Dmitri Panov | The following statement is a bit suspicious: "Then it can be checked that $g_{L,K}=...$ ... is balloon map...". For example, if $K$ and $L$ are perpendicular, and $f$ is identical, as far as I can see $g_{L,K}$ is a projection from $L$ to a point on $K$. This is not balloon... Could you give a justification of this statement? | |
| Jan 6, 2019 at 20:53 | history | edited | Martin Kell | CC BY-SA 4.0 |
added 1517 characters in body
|
| Jan 4, 2019 at 15:55 | comment | added | Martin Kell | @DmitriPanov, you are right, I missed that point. A quick check, only gave that the image of closed ball is the closed ball, i.e. $f(\bar U) = \overline{f(U)}$. Via a contradiction argument it is also possible to prove that a half space is mapped to a half space and that $f$ has to be surjective. This would rescue the convexity property. Currently I see a problem that the two touching points at the boundary of the big ball might not get mapped onto the boundary of the image of the large ball. Maybe the half-space property is sufficient to prove this. I'll try to fix it as soon as possible. | |
| Jan 4, 2019 at 13:31 | comment | added | Dmitri Panov | This proof seems to use the following fact from the very beginning: $f$ sends the boundary of each open ball $U$ to the the boundary of the image $f(U)$. Such a property is not assumed in the original question, so it should be proven first, it seems to me. | |
| Jan 4, 2019 at 11:26 | history | answered | Martin Kell | CC BY-SA 4.0 |