Timeline for Are all manifolds affine?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 20, 2012 at 11:43 | comment | added | David Carchedi | Of course, now that I see that the Hausdorff condition cannot be removed, I am still curious if one can keep the Hausdorff condition, and remove paracompactness. | |
| Feb 20, 2012 at 11:24 | comment | added | David Carchedi | @Taladris: FYI, for a functor to me an embedding, it means that it is full and faithful, i.e.,I want to know if the natural map $$C^{\infty}\left(M,N\right) \to \Hom\left(C^{\infty}\left(N\right),C^{\infty}\left(N\right)\right)$$ is a bijection. Of course, what you wrote implies this cannot be the case, I just wanted to clarify for you. | |
| Feb 20, 2012 at 11:21 | comment | added | David Carchedi | @Mariano: Actually, I would like to see what I can get away with. At any rate, both paracompactness and Hausdroffness are needed for partiions of unity, and also for Whitney's embedding theorem. I wanted to see how far away from (either of) these assumptions the theorem still holds. | |
| Feb 20, 2012 at 5:26 | comment | added | Mariano Suárez-Álvarez | The hypothesis David wants to remove is paracompactness, not Hausdorffness. | |
| Feb 20, 2012 at 4:26 | history | answered | Taladris | CC BY-SA 3.0 |