Canonical equivalence relations on nets of PSc0PSc0

We give a list of canonical equivalence relations on discrete nets of the positive unit sphere of c0c0. This generalizes results of W.T. Gowers [Lipschitz functions on classical spaces, European J. Combin. 13 (1992) 141–151] and A.D. Taylor [A canonical partition relation for finite subsets of ωω. J. Combin. Theory Ser. A 21(2) (1976) 137–146].