Timeline for Any reference including a coordinate free proof of the inverse function theorem? [closed]
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 15, 2019 at 3:37 | comment | added | ZxJx | Should I delete this question and repost it on MSE? | |
| Nov 14, 2019 at 12:35 | history | closed |
LSpice Ben McKay David Handelman Alex M. ARG |
Not suitable for this site | |
| Nov 12, 2019 at 12:09 | comment | added | Liviu Nicolaescu | See section 14.3 of these notes www3.nd.edu/~lnicolae/Hon_Calc_Lectures.pdf | |
| Nov 12, 2019 at 3:45 | review | Close votes | |||
| Nov 14, 2019 at 12:35 | |||||
| Nov 12, 2019 at 3:26 | comment | added | LSpice | This seems like a great goal to further your understanding, but very much not a research-level question, so that it does not belong here. | |
| Nov 11, 2019 at 21:55 | comment | added | Deane Yang | Or look up the implicit function theorem in any text on functional analysis, where it will be proved for infinite dimensional Banach spaces. The proof is virtually the same. | |
| Nov 11, 2019 at 20:57 | answer | added | Pietro Majer | timeline score: 0 | |
| Nov 11, 2019 at 20:39 | vote | accept | ZxJx | ||
| Nov 11, 2019 at 20:39 | vote | accept | ZxJx | ||
| Nov 11, 2019 at 20:39 | |||||
| Nov 11, 2019 at 20:28 | answer | added | Dmitri Pavlov | timeline score: 2 | |
| Nov 11, 2019 at 20:26 | comment | added | ZxJx | Also, thank you both, that has answered my question :) | |
| Nov 11, 2019 at 20:19 | comment | added | ZxJx | By baby Rudin, you mean "Principles..." right? I don't hate coordinates!!! Coordinates help us to visualize and understand things, and coordinate-free is another way. I don't think of one as better than the other, just different points of view, different organizations for calculations. Just as some coordinate systems facilitate calculations over other coordinate (e.g. spherical vs rectilinear) | |
| Nov 11, 2019 at 20:12 | comment | added | Abdelmalek Abdesselam | why so much hate for coordinates... | |
| Nov 11, 2019 at 19:53 | comment | added | user131781 | The inverse function theorem holds for functions between Banach spaces. The essential ingredient in the proof is the Banach fixed point theorem. In this situation, the proof must needs be coordinate-free. Off-hand, I am fairly sure that this can be found, for example, in Dieudonné‘s multi-volumed „Treatise on Analysis“. | |
| Nov 11, 2019 at 19:43 | comment | added | Alexandre Eremenko | "Baby Rudin" is a good book. | |
| Nov 11, 2019 at 19:21 | history | asked | ZxJx | CC BY-SA 4.0 |