Timeline for Metric "in the limit"?
Current License: CC BY-SA 4.0
5 events
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| Nov 13, 2020 at 19:29 | comment | added | Gabe K | In order to be amenable to discrete topologies, you might want to switch the order of $x$ and $\epsilon $ in that definition of "going to infinity" so that the $\epsilon $ may depend on $x$. That will be equivalent to your definition if the topology induced by $d(x, \cdot)$ is discrete. | |
| Nov 13, 2020 at 19:23 | history | edited | Gabe K | CC BY-SA 4.0 |
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| Nov 13, 2020 at 19:21 | comment | added | Gabe K | That's a good point. I'll edit the answer to acknowledge that. | |
| Nov 13, 2020 at 18:02 | comment | added | Bjørn Kjos-Hanssen | Your displayed equation is not formally a strengthening, but rather incomparable to mine I guess? I didn't say it but I was thinking of a bounded space, $\exists c\forall x,y\, d(x,y)\le c$, which is maybe a different direction than you're going in. Still, thanks for the food for thought. | |
| Nov 13, 2020 at 17:00 | history | answered | Gabe K | CC BY-SA 4.0 |