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Oct
4
awarded  Inquisitive
Oct
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awarded  Popular Question
Sep
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awarded  Popular Question
Jul
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awarded  Nice Question
Jan
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Aug
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Jul
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awarded  Curious
Mar
25
asked Derivation of the advection equation
Mar
17
awarded  Popular Question
Aug
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awarded  Yearling
Feb
28
revised Good metric on $C^k(0,1)$ and $C^\infty(0,1)$
added 193 characters in body
Feb
28
revised Good metric on $C^k(0,1)$ and $C^\infty(0,1)$
added 193 characters in body
Feb
28
answered Good metric on $C^k(0,1)$ and $C^\infty(0,1)$
Feb
28
comment Good metric on $C^k(0,1)$ and $C^\infty(0,1)$
It is important to you that the interval your functions live on is open, right? If it would be closed like in $C^k([0,1])$, you could get a norm on this space that even makes it a Banach space. (And every norm induces a metric). That would be a rather good metric on $C^k([0,1])$ in my opinion. I don't know about the $C^{\infty}$-case though...
Feb
27
accepted Is every open, bounded and simply connected subset of $\mathbb{R}^n$ essentially a ball?
Feb
26
asked The simplicity of $\bigwedge^i \mathbb{C}^{n+1}$ as a representation of $\mathfrak{sl_{n+1}}$ and its weight vectors
Feb
19
accepted Do we really need Hahn-Banach that much?
Feb
19
comment Do we really need Hahn-Banach that much?
Okay, thank you! Makes me kind of sad, though... ;)
Feb
19
comment Do we really need Hahn-Banach that much?
Of course - didn't see that until now. That might prove a problem... :)
Feb
19
comment Do we really need Hahn-Banach that much?
Since every $x\in X$ can be written uniquely as $x=y+c$ for $y\in Y$ and $c\in C$, we have $\|y'(x)\|=\|y'(y)\|\le \operatorname{sup}_Y$, so $\operatorname{sup}_X\le \operatorname{sup}_Y$.