Dimension in a reasonable class of spaces

Let P be a class of compact spaces satisfying:(a) losed with respect to taking finite products. losed with respect to taking closed subspaces. ains all metrizable compacta. member of P can be mapped onto a metrizable space by a zero-dimensional map. distinct dimension functions coincide on completely paracompact subspaces of members of P, and each subspace of a member of P has a compactification in P of the same weight and dimension. Examples of classes satisfying (a), (b), (c) and (d) are several classes of Eberlein compactifications of metrizable spaces. There are, however, uniform Eberlein compacta with dim < ind .