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This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*‐modules over commutative C*‐algebras. When the fiber dimensions differ sufficiently, relative to the dimension of the spectrum, we show that there is an embedding between the modules. This result continues to hold over recursive subhomogeneous C*‐algebras. For certain modules, including all modules over  C  0 ( X ) when dim  X  ⩽ 3, isomorphism and embedding are determined by the restrictions to the sets where the fiber dimensions are constant. These considerations yield results for the Cuntz semigroup, including a computation of the Cuntz semigroup for  C  0 ( X ) when dim  X  ⩽ 3, in terms of cohomological data about  X .

Hilbert C*‐modules over a commutative C*‐algebra

Hilbert C‐modules over a commutative C‐algebra