Timeline for Locally constant functions with compact support = smooth ?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 9, 2011 at 13:13 | vote | accept | Thomas | ||
| May 9, 2011 at 2:21 | comment | added | LSpice | Actually I was rather sloppy: “wandering around” doesn't suggest the need to go very far, but the local compactness of $\mathbb Q_p$ means that I should have said that we were considering balls with centres tending to $\infty$. (I have at least avoided referring to the centre of a ball, that being an eminently Archimedean concept.) | |
| May 8, 2011 at 21:22 | comment | added | Justin Campbell | @L Spice: Yes, I was picturing something like this but didn't want to trust my intuition in this non-Archimedean setting... | |
| May 8, 2011 at 18:06 | comment | added | LSpice | Justin, for a locally constant but not uniformly locally constant function, just consider a sum of characteristic functions of balls with radii tending to 0, and centres wandering around (i.e., no cluster points). | |
| May 8, 2011 at 4:23 | comment | added | Joël Cohen | Yes, you're right about the distinction between invariant by an open subset and locally constant. Sorry for my mistake. | |
| May 8, 2011 at 4:03 | history | answered | Justin Campbell | CC BY-SA 3.0 |