Timeline for Can we construct a surjective mapping from $\mathbb{R}^{?}$ to this space?
Current License: CC BY-SA 4.0
7 events
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| Nov 23, 2020 at 11:33 | comment | added | lrnv | @LSpice Yeah a simple projection on the space works, but, and this is my mistake for not specifying it before, i'd like something that is smooth, and not only continuous. Like if you optimize on the positive reals, then optimizing on the log makes your problem unconstraint. | |
| Nov 19, 2020 at 20:59 | comment | added | LSpice | It's not clear what the quantifiers are in the definition of $S$, but I guess you first pick $C$ and then define $S_C$. Then $S_C$ is compact and convex, and you can just project from the ambient Euclidean space on it; this gives a continuous map (from a higher-dimensional space). | |
| Nov 19, 2020 at 20:58 | comment | added | LSpice | I think @DieterKadelka's point is that $p = 1$ not just probably works, but proveably works (it's just testing cardinalities), if you just ask for a surjective mapping of sets. | |
| Nov 19, 2020 at 19:07 | comment | added | lrnv | Probably p=1 does the job, but i would prefer something like $p = n^d - nd - 1$ which is the number of degree of freedom in my equations. If you have a surjective mapping for p=1, please tel me anyway. | |
| Nov 19, 2020 at 17:03 | comment | added | Dieter Kadelka | What type of mapping do you want? Otherwise $p = 1$ does the job ($S$ and $\mathbb{R}$ have the same cardinality. | |
| Nov 19, 2020 at 16:03 | history | edited | lrnv |
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| Nov 19, 2020 at 15:53 | history | asked | lrnv | CC BY-SA 4.0 |