The homotopy fiber of profinite completion

We show that the basepoint-component of the homotopy fiber of Sullivan's profinite completion map c: Y --> (Y) over cap is always an H-space, provided Y is nilpotent of finite type. This observation allows for a reworking of the completion/rationalization approach to phantom map theory and leads to more direct, transparent proofs of various results in the recent literature on phantom maps. (C) 2000 Elsevier Science B.V. All rights reserved.