Stability in the Cuntz semigroup of a commutative C*-algebra

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.

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