Fell topology

Summary

The Fell topology is the natural topology on the unitary dual of a locally compact group, the set of equivalence classes of irreducible unitary representations. A representation lies in the closure of a set of representations when it is weakly contained in that set. This means that its matrix coefficients can be approximated by those of the set. It agrees with the hull-kernel topology of the spectrum of the group C*-algebra. For abelian groups it is the usual topology of the Pontryagin dual, but in general it need not be Hausdorff.