22 JONATHAN ROSENBERG AND CLAUDE SCHOCHET

possible in the case of G = Tn and, in particular, if G = T.

COROLLARY 2.10. Suppose that G is a torus (of any dimension). Let

F be the collection of G-algebras of the form C(G/H,w), where H

is a closed subgroup of G and w is a G/H cocycle. Then F is a

CQ-fundamental family.

PROOF: This follows from Theorems 2.5 and 2.8. •

COROLLARY 2.11. If G = T, the G-algebras of the form C(G/H) ,

where H = {1}, Z , or G, are a CQ-fundamental family.

2

PROOF: For any closed subgroup HofT, HM(H,T) =0. a

COROLLARY 2.12. If G = T, then BQ = CQ/ and if G = S0(2), then

^G - CG-

PROOF; This is a restatement of (2.11). D