A non-computable c.e. closed subset of $[0,1]$

Serikzhan Badaev, Nikolay Bazhenov, Sergey Goncharov +2

We prove that there exists a $\hat{I}{\pounds }_1^0$ closed subset of $[0,1]$ that is not homeomorphic to any computably compact space. We show that the index set of c.e. subspaces of $[0,1]$ tha…