Timeline for Growth function of locally compact groups
Current License: CC BY-SA 3.0
9 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 16, 2017 at 20:39 | comment | added | LSpice | @YCor, ah, of course that's true; how embarrassing. I think I answered the original question (can the growth function be discontinuous?) positively, and satisfied 'propriety' and non-discreteness, but, as you point out, did not satisfy the additional condition that the closure of an open ball is the corresponding closed ball (although I incorrectly said that I did). | |
| Feb 16, 2017 at 20:28 | comment | added | YCor | I actually don't know which question you claim to answer. | |
| Feb 16, 2017 at 20:22 | comment | added | YCor | But in the additive group, the open 1-ball is closed, i.e. equal to its closure, but not equal to the "closed 1-ball". | |
| Feb 16, 2017 at 20:16 | history | edited | LSpice | CC BY-SA 3.0 |
Wrong claim modified to be less ambitious, and hopefully right
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| Feb 16, 2017 at 20:14 | comment | added | LSpice | @YCor, oh, right, I ignored the crucial 'left-invariant' part. I guess the additive group (with its usual metric) should still work, though. | |
| Feb 16, 2017 at 19:56 | comment | added | YCor | And clearly $\mathbf{Q}_p^*$ admits no proper compatible left-invariant ultrametric. | |
| Feb 16, 2017 at 19:54 | comment | added | YCor | You need to specify the metric on the multiplicative group. | |
| Feb 16, 2017 at 19:46 | history | answered | LSpice | CC BY-SA 3.0 |