  I. Raeburn and J. Taylor have constructed continuous-trace C*-algebras with a
prescribed Dixmier-Douady class, which also depend on the choice of an open
cover of the spectrum. We study the asymptotic behavior of these algebras with
respect to certain refinements of the cover and appropriate extension of
cocycles. This leads to the analysis of a limit groupoid G and a cocycle
\sigma, and the algebra C*(G, \sigma) may be regarded as a generalized direct
limit of the Raeburn-Taylor algebras. As a special case, all UHF C*-algebras
arise from this limit construction.
