Every gauge orbit passes inside the Gribov horizon

TheL² topology is introduced on the space of gauge connectionsA and a natural topology is introduced on the group of local gauge transformationsGT. It is shown that the mappingGT×AA defined byAA^g=g^*Ag+g^*dg is continuous and that each gauge orbit is closed. The Hilbert norm of the gauge connection achieves its absolute minimum on each gauge orbit, at which point the orbit intersects the region bounded by the Gribov horizon.CNR, GNFMResearch supported in part by the National Science Foundation under grant no. PHY 87-15995