Topologically invariant $σ$-ideals on the Hilbert cube

英文摘要：

We study and classify topologically invariant $σ$-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.