Topologically invariant $σ$-ideals on the Hilbert cube

Taras Banakh, Michal Morayne, Robert Ralowski, Szymon Zeberski

Published 2013-02-22, updated 2014-09-13Version 3

We study and classify topologically invariant $\sigma$-ideals with a Borel base on the Hilbert cube and evaluate their cardinal characteristics. One of the results of this paper solves (positively) a known problem whether the minimal cardinalities of the families of Cantor sets covering the unit interval and the Hilbert cube are the same.