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Jul 9, 2019 at 18:52 comment added Pietro Majer And let's add that $1/n$ is the best exponent: any $\alpha$-Hölder curve $[0,1]\to[0,1]^n$ with $\alpha>1/n$ can't be surjective.
Mar 29, 2019 at 0:31 vote accept Christian Chapman
Apr 20, 2018 at 3:43 comment added Piotr Hajlasz I do not know the reference on top of my head. Just Google: Peano curve Holder exponent.
Apr 20, 2018 at 3:33 comment added Christian Chapman Thanks. Do you know anywhere these things are constructed and proven?
Apr 20, 2018 at 3:16 history answered Piotr Hajlasz CC BY-SA 3.0