Timeline for About filters on real numbers
Current License: CC BY-SA 3.0
6 events
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| May 21, 2017 at 21:57 | comment | added | Olivier Bégassat | If you take $X=\lbrace-\frac{1}{n+1}\mid n\in\Bbb{N}\rbrace$, then for any sequence $\epsilon_n$ of positive real numbers the intersection you consider contains the set $$\bigcup_{n\in\Bbb{N}}\left[-\frac1{n+1},-\frac1{n+1}+\epsilon_n\right)$$ which can can have total length $\leq\sum_n\epsilon_n$ shorter than any $\delta>0$. So the intersection isn't included in any such principal filter. | |
| May 21, 2017 at 21:52 | history | edited | porton | CC BY-SA 3.0 |
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| May 21, 2017 at 21:45 | history | edited | porton | CC BY-SA 3.0 |
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| May 21, 2017 at 21:34 | review | Close votes | |||
| May 22, 2017 at 2:23 | |||||
| May 21, 2017 at 21:12 | history | edited | porton | CC BY-SA 3.0 |
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| May 21, 2017 at 21:05 | history | asked | porton | CC BY-SA 3.0 |