UNIVERSAL SPACES IN THE THEORY OF TRANSFINITE DIMENSION .2.

We construct a family of spaces with ''nice'' structure which is universal in the class of all compact metrizable spaces of large transfinite dimension omega(0), or, equivalently, of small transfinite dimension omega(0); that is, the family consists of compact metrizable spaces whose transfinite dimension is omega(0), and every compact metrizable space with transfinite dimension omega(0) is embeddable in a space of the family. We show that the least possible cardinality of such a universal family is equal to the least possible cardinality of a dominating sequence of irrational numbers.