## Real Analysis Exchange

### The Class of Purely Unrectifiable Sets in $\ell_2$ is $\Pi_1^1$-complete

#### 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 $\Pi_1^1$-complete.

#### Article information

Source
Real Anal. Exchange, Volume 39, Number 2 (2014), 323-334.

Dates
First available in Project Euclid: 30 June 2015

Kulikov, Vadim. The Class of Purely Unrectifiable Sets in $\ell_2$ is $\Pi_1^1$-complete. Real Anal. Exchange 39 (2014), no. 2, 323--334. https://projecteuclid.org/euclid.rae/1435669998