Timeline for Intersection of nested open ball in complete metric spaces is nonempty?
Current License: CC BY-SA 4.0
13 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Sep 29, 2018 at 19:04 | comment | added | Brian | @M.Dus Please refer to the link on the last line in the original post. | |
| Sep 29, 2018 at 15:42 | comment | added | M. Dus | @Syuizen What is your example for which $\overline{B(x_{i+1},r_{i+1})}\subset B(x_i,r_i)$ and $\bigcap B(x_i,r_i)=\emptyset$ ? | |
| Sep 29, 2018 at 12:02 | history | edited | Martin Sleziak |
added the (metric-spaces) tag
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| Sep 28, 2018 at 5:28 | vote | accept | Brian | ||
| Sep 28, 2018 at 3:41 | answer | added | Nik Weaver | timeline score: 8 | |
| Sep 28, 2018 at 2:20 | history | edited | Brian | CC BY-SA 4.0 |
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| Sep 28, 2018 at 2:00 | comment | added | Brian | @YemonChoi Cantor's lemma requires either the compactness of closed bounded set or diameter of closed sets tend to 0. However, you may not have these based on given information in a general metric space. | |
| Sep 28, 2018 at 1:44 | comment | added | Yemon Choi | Isn't this just Cantor's lemma once you look at the closed ball centred on $x_{i+1}$ with radius $1+\varepsilon/2$? | |
| Sep 28, 2018 at 1:34 | comment | added | Brian | @erz Sorry about the confusion. I have edited it to make it clear. Basically, I don't know if the statement given in the beginning is true or not. (I intuitively believe it is true). | |
| Sep 28, 2018 at 1:31 | history | edited | Brian | CC BY-SA 4.0 |
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| Sep 28, 2018 at 1:17 | comment | added | erz | so what is the question? | |
| Sep 28, 2018 at 0:58 | history | asked | Brian | CC BY-SA 4.0 |