  We prove stability theorems in the Cuntz semigroup of a commutative
C*-algebra which are analogues of classical stability theorems for topological
vector bundles over compact Hausdorff spaces. Several applications to simple
unital AH algebras of slow dimension growth are then given: such algebras have
strict comparison of positive elements; their Cuntz semigroups are recovered
functorially from the Elliott invariant; the lower-semicontinuous dimension
functions are dense in the space of all dimension functions, and the latter is
a Choquet simplex.
