  It is shown that a C*-algebra of the form C(X,U), where U is a UHF algebra,
is not an inductive limit of subhomogeneous C*-algebras of topological
dimension less than that of X. This is in sharp contrast to dimension-reduction
phenomenon in (i) simple inductive limits of such algebras, where
classification implies low-dimensional approximations, and (ii) when dimension
is measured using decomposition rank, as the author and Winter proved that
dr(C(X,U)) $\leq$ 2.
