Strongly countable dimensional compacta form the Hurewicz set

The hyperspaces of strongly countable dimensional compacta of positive dimension and of strongly countable dimensional continua of dimension greater than 1 in the Hilbert cube are homeomorphic to the Hurewicz set of all nonempty countable closed subsets of the unit interval [ 0 , 1 ] . These facts hold true, in particular, for covering dimension dim and cohomological dimension dim G , where G is any Abelian group.