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The Class of Purely Unrectifiable Sets in the Hilbert Space is coanalytic-complete
Preprint
2013-03-14
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Abstract
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.