On D-dimension of metrizable spaces*

For every cardinal τ and every ordinal α, we construct a metrizable space Mα(τ) and a strongly countable-dimensional compact space Zα(τ) of weight τ such that D(Mα(τ)) ≤ α, D(Zα(τ)) ≤ α and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of Mα(τ) and to a subspace of Zα+1(τ).