The Dixmier-Douady class and an abelian extension of the homeomorphism group

Let X be a connected topological space and c∈H2(X;Z) non-zero cohomology class. A Homeo(X,c)-bundle is fiber bundle with whose structure group reduces to the Homeo(X,c) of c-preserving homeomorphisms X. If H1(X;Z)=0, then characteristic class for Homeo(X,c)-bundles called Dixmier-Douady defined via Serre spectral sequence. We show relation between universal foliated gauge extension Homeo(X,c). Moreover, under some assumptions, we construct central S1-extension two-cocycle on corresponding