Timeline for Is there a Borel-measurable function which maps every interval onto $\mathbb R$?
Current License: CC BY-SA 4.0
7 events
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| Nov 30, 2019 at 18:33 | comment | added | Vladimir Kanovei | I have to thank everybody for comprehensive answers. A bit more complex question could be to require that the $F$-preimage of every singleton be a COUNTABLE dense set. | |
| Nov 30, 2019 at 18:06 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
corrected a link
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| Nov 30, 2019 at 17:11 | comment | added | Martin Sleziak | @GregoryArone You're right about that. (And I should have been more careful when writing the answer.) Luckily enough, a Borel function is enough for the requirements of the asker. (For example, we can take a continuous bijection $(0,1)\to\mathbb R$ and define values at $0$ and $1$ arbitrarily. | |
| Nov 30, 2019 at 17:10 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
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| Nov 30, 2019 at 17:06 | comment | added | Gregory Arone | How can there be a continuous surjection from the compact interval $[0,1]$ to the reals? | |
| Nov 30, 2019 at 16:44 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
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| Nov 30, 2019 at 15:49 | history | answered | Martin Sleziak | CC BY-SA 4.0 |