Timeline for Uncountable preimage of every point
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2010 at 19:27 | comment | added | André Henriques | Every point-preimage is an intersection of subsets of the following form: essentially disjoint unions of $2^n$ intervals, each one of them having a length of $2^{-2n}$. To go from one of these subsets to the next one, you replace every interval of length $2^{-2n}$ by two sub-intervals of length $2^{-(2n+2)}$. | |
| Nov 28, 2010 at 7:25 | comment | added | Nikita Kalinin | @André Henriques Could you clarify it, please? | |
| Nov 28, 2010 at 0:39 | comment | added | André Henriques | If you take the standard example of a space filling curve, and do what Reid and Mark sudgested, then no point-preimage has Hausdorff dimension zero. They actually all have the same Hausdorff dimension: 1/2. | |
| Nov 27, 2010 at 20:43 | history | answered | Reid Barton | CC BY-SA 2.5 |