Timeline for Control on dimension of image
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2021 at 14:45 | comment | added | ABIM | @JochenGlueck Fair enough; I was just having fun with over-powered ways to show simple things (like just keeping track of the basis of the image under the linear map) | |
| Jan 19, 2021 at 14:38 | comment | added | Jochen Glueck | @Wasserstein'sApprentice: Thanks for your reply! I'm just wondering why you would like to apply the splitting lemma here: a linear image of a finite-dimensional space is obviously finitely generated and thus finite-dimensional - so no need to split anything ;-). But admittedly, that's a bit nitpicking, and it leads away from your actual question. | |
| Jan 19, 2021 at 12:42 | vote | accept | ABIM | ||
| Jan 19, 2021 at 12:17 | comment | added | ABIM | I mean, the linear algebraic splitting lemma to infer that the image of $f$ (if linear) is a finite-dimensional subspace of its codomain; then you use the fact that maps between finite-dimensional linear spaces are (weakly) continuous...so any linear map is strong-weakly continuous and has finite dimensional image | |
| Jan 19, 2021 at 11:58 | comment | added | Jochen Glueck | @Wasserstein'sApprentice: Just curious: what do you mean by "splitting lemma" in this context?) | |
| Jan 19, 2021 at 11:42 | vote | accept | ABIM | ||
| Jan 19, 2021 at 11:42 | |||||
| Jan 19, 2021 at 11:37 | answer | added | Stefan Waldmann | timeline score: 5 | |
| Jan 19, 2021 at 11:24 | comment | added | ABIM | @JochenWengenroth The first part I also noticed (obv. from splitting lemma) and I expect the second may follow for weak-strong continuous maps which are sufficiently Frechet differentiable.. | |
| Jan 19, 2021 at 10:17 | comment | added | Jochen Wengenroth | For linear maps this is trivial and for non-linear maps this seems to be hopeless. | |
| Jan 19, 2021 at 7:56 | history | asked | ABIM | CC BY-SA 4.0 |