  Let G be one of the local gauge groups C(X,U(n)), C^\infty(X,U(n)),
C(X,SU(n)) or C^\infty(X,SU(n)) where X is a compact Riemannian manifold. We
observe that G has a nontrivial group topology, coarser than its natural
topology, w.r.t. which it is amenable, viz the relative weak topology of
C(X,M(n)). This topology seems more useful than other known amenable topologies
for G. We construct a simple fermionic model containing an action of G,
continuous w.r.t. this amenable topology.
