Timeline for extracting a convergence subnet from a sequence which is Cauchy on every bounded subset of $\mathbb N$.
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 5, 2013 at 17:09 | comment | added | Nate Eldredge | Unless I am missing something, in a metric space (or any first countable space), shouldn't any sequence with a convergent subnet also have a convergent subsequence? So "subnet" here seems to be a red herring. | |
| Jan 18, 2012 at 17:04 | answer | added | Pietro Majer | timeline score: 3 | |
| Jan 18, 2012 at 15:49 | comment | added | Valerio Capraro | Well, to exclude existence of convergent subsequences, it should be enough to take $x_n$ such that $d(x_n,x_m)=\frac{m−n}{n}$, for all $m\geq n$. It verifies the hypotheses above but has no Cauchy subsequences... subnets? | |
| Jan 18, 2012 at 15:48 | answer | added | Andreas Blass | timeline score: 8 | |
| Jan 18, 2012 at 14:37 | history | asked | Valerio Capraro | CC BY-SA 3.0 |