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2013/2014 The Class of Purely Unrectifiable Sets in \(\ell_2\) is \(\Pi_1^1\)-complete
Vadim Kulikov
Real Anal. Exchange 39(2): 323-334 (2013/2014).


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 \(\Pi_1^1\)-complete.


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Vadim Kulikov. "The Class of Purely Unrectifiable Sets in \(\ell_2\) is \(\Pi_1^1\)-complete." Real Anal. Exchange 39 (2) 323 - 334, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 30 June 2015

zbMATH: 1354.03064
MathSciNet: MR3365377

Primary: 03E15 , 28A05
Secondary: 28E15

Keywords: co-analytic complete , Hilbert space , Purely unrectifiable

Rights: Copyright © 2014 Michigan State University Press

Vol.39 • No. 2 • 2013/2014
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