Timeline for On the existence of a sequence of positive continuous functions
Current License: CC BY-SA 2.5
7 events
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| Aug 3, 2010 at 16:27 | history | edited | Roland Bacher | CC BY-SA 2.5 |
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| Aug 3, 2010 at 15:34 | comment | added | Roland Bacher | That is disturbing! | |
| Aug 3, 2010 at 15:09 | comment | added | Malik Younsi | I don't see how that would be possible... The paper cited below proves the following result : There is a sequence of continuous functions on $[0,1]$ whose pointwise limit if finite on $S$ and infinite on the complement of $S$ if and only if $S$ is a $F_{\sigma}$. But $\mathbb{R} \setminus \mathbb{Q}$ is not a $F_{\sigma}$, so the sequence of functions you're trying to construct cannot exist... | |
| Aug 3, 2010 at 14:31 | comment | added | Roland Bacher | True. One has to choose the sequence $s_n$ suitably in order to avoid this. | |
| Aug 3, 2010 at 14:20 | comment | added | Malik Younsi | I don't understand. Isn't it possible that $s_n(d(x,\mathbb Q_n))$ tends to infinity for some irrational $x$? | |
| Aug 3, 2010 at 13:12 | history | edited | Roland Bacher | CC BY-SA 2.5 |
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| Aug 3, 2010 at 13:03 | history | answered | Roland Bacher | CC BY-SA 2.5 |