Timeline for Smooth Urysohn's lemma on Fréchet spaces
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2023 at 15:39 | vote | accept | André Henriques | ||
| Nov 1, 2023 at 22:49 | history | became hot network question | |||
| Nov 1, 2023 at 21:34 | answer | added | Alexander Schmeding | timeline score: 9 | |
| Nov 1, 2023 at 17:57 | answer | added | Pietro Majer | timeline score: 11 | |
| Nov 1, 2023 at 17:55 | comment | added | Alexander Schmeding | @AndréHenriques: note that on Frechet spaces, frechet smoothness makes no sense and you either need convenient smooth maps or (equivalent on frechet spaces) Bastiani smoothness. | |
| Nov 1, 2023 at 17:52 | comment | added | Alexander Schmeding | Actually smooth paracompactness is strenger than what you need. The condition would be smooth regularity (which is weaker than smooth paracompactness). Also for this conditions are know and recorder for example in kriegl/michor | |
| Nov 1, 2023 at 17:50 | comment | added | Alexander Schmeding | Adendum: I think the proofs for smooth paracompactness of the spaces you are interested in can be traced back at least to Michors old book: Manifolds of Differentiable mappings (both book are available on michors Homepage) | |
| Nov 1, 2023 at 17:48 | comment | added | Alexander Schmeding | For these it works as spaces of smooth function are on compact spaces are know to be smoothly paracompact. All of this is recorder in Detail with Conditions in Kriegl/Michor: The convenient setting of global Analysis. | |
| Nov 1, 2023 at 17:26 | comment | added | André Henriques | @PietroMajer. Your comment seems to answer my question in the negative. I would be happy to accept it if you wrote it as an answer. But I am more interested in positive results. Are there conditions that one can impose on a Banach space that ensure that the smooth Urysohn's lemma holds true for functions on that Banach space? (The kind of Fréchet space I need this for is $C^\infty(M)$, for $M$ some compact manifold.) | |
| Nov 1, 2023 at 17:24 | history | edited | André Henriques | CC BY-SA 4.0 |
deleted 2 characters in body
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| Nov 1, 2023 at 17:24 | comment | added | André Henriques | @WillieWong Yes, of course, I meant subsets. | |
| Nov 1, 2023 at 16:33 | history | edited | LSpice | CC BY-SA 4.0 |
Typo
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| Nov 1, 2023 at 16:10 | comment | added | Iosif Pinelis | @PietroMajer : Could you provide references to such Banach spaces? | |
| Nov 1, 2023 at 15:59 | comment | added | Pietro Majer | The fact is that there are Banach spaces with no non-zero C¹ functions with bounded support. In this situation the best partition of unity we can do are loc.lip, and we should be happy, since loc.lip is sufficient for building flows via ODE. | |
| Nov 1, 2023 at 14:49 | history | asked | André Henriques | CC BY-SA 4.0 |