The Class of Purely Unrectifiable Sets in the Hilbert Space is coanalytic-complete

preprint2013arXivOpen access

The space $F(\ell_2)$ of all closed subsets of $\ell_2$ is a Polish space. We show that the subset $P\subset F(\ell_2)$ consisting of the purely 1-unrectifiable sets is $\Pii$-complete.

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The Class of Purely Unrectifiable Sets in the Hilbert Space is coanalytic-complete

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