Local triviality for continuous field C^∗-algebras

© The Author(s) 2013. Let X be a finite-dimensional compact metrizable space. Let Abe a separable continuous field C∗-algebra over X with all fibers isomorphic to the same stable Kirchberg algebra D. We show that if D has finitely generated K-theory and it satisfies the Universal Coefficient Theorem in KK-theory, then there exists a dense open subset U of X such that the ideal A(U) is locally trivial. The assumptions that the space X is finite-dimensional and that the K-theory of the fiber is finitely generated are both necessary.