The hyperspace of hereditarily decomposable subcontinua of a cube is the Hurewicz set
It is shown that the hyperspace \(\mathcal{HD}(I^n)\) of hereditarily decomposable subcontinua of the cube \(I^n\) of finite or infinite dimension \(n\geq 3\) is an absorbing space for coanalytic spaces. Consequently, \(\mathcal{HD}(I^n)\) is homeomorphic to the Hurewicz space \(\mathcal{H}\) of all non-empty countable closed subsets in \([0,1]\). The same it true for the space \(\mathcal{DNP}(I^n)\) of decomposable subcontinua of \(I^n\) that contain no copy of the pseudoarc: \(\mathcal{DNP}(I^n)\) is homeomorphic to \(\mathcal H\).
scientific article; zbMATH DE number 5131627