Timeline for What is the usual topology of $C^\infty_c(M) $
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 20, 2014 at 8:46 | history | edited | user9072 |
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| Aug 3, 2012 at 5:03 | vote | accept | Adterram | ||
| Apr 27, 2012 at 18:38 | comment | added | Mariano Suárez-Álvarez | Todd: smoothly truncating $e^{-x^2}$ on $\mathbb R$ so as to obtain a sequence of compactly supported functions appropriately should give a Cauchy sequence in that metric which does not converge, no? | |
| Apr 27, 2012 at 17:50 | comment | added | Todd Leason | Added: $K$ has to be taken to include the support of $f,g$. | |
| Apr 27, 2012 at 17:46 | comment | added | Todd Leason | I don't know if this is usual, but it should be possible to define a metric by $$d(f,g) = \sum_n \frac{1}{2^{n+A(n)}}\sum_{|\alpha|=n}\frac{\left|\sup_K\frac\partial{\partial x^\alpha}(f-g)\right|}{1 + \left|\sup_K\frac\partial{\partial x^\alpha}(f-g)\right|}$$ where $A(n)$ is the number of $\alpha$ s.t. $|\alpha|=n$. The space should be complete in the induced topology. | |
| Apr 27, 2012 at 17:28 | answer | added | John Pardon | timeline score: 24 | |
| Apr 27, 2012 at 16:29 | comment | added | Zev Chonoles | Crossposted to math.SE: math.stackexchange.com/q/137701/264 | |
| Apr 27, 2012 at 16:18 | history | asked | Adterram | CC BY-SA 3.0 |