Timeline for Is there a Borel-measurable function which maps every interval onto $\mathbb R$?
Current License: CC BY-SA 4.0
5 events
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| Dec 1, 2019 at 12:18 | history | edited | bof | CC BY-SA 4.0 |
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| Dec 1, 2019 at 12:10 | history | edited | bof | CC BY-SA 4.0 |
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| Dec 1, 2019 at 12:06 | comment | added | bof | Sounds right. Hmm. What if we define $f(x)=x$ for $x\notin\bigcup_nA_n$? | |
| Dec 1, 2019 at 11:26 | comment | added | Martin Sleziak | If we choose the function $f_n$ in a manner similar to Devil's staircase, we get that $f^{-1}(x)$ is countable for each $x\ne0$, right? (For each $x$ we get at most two preimages inside $A_n$.) I am asking this since Vladimir Kanovei mentioned in a comment that they would also be interested in an example where the fibers are countable dense sets. | |
| Dec 1, 2019 at 11:17 | history | answered | bof | CC BY-SA 4.0 |