A whitehead theorem for long towers of spaces

We show that one can construct the universalR-homology isomorphismK →E _RX of Bousfield 1] by a transfinite iteration of an elementary homology correction map. This correction map is essentially the same as the one used classically to define Adams spectral sequence. This yields a topological characterization of the class of local spaces as the smallests containingK(A, n)’s and closed under homotopy inverse limit. This research was partially supported by the National Science Foundation, Grant # MCS76-08795, and by the U.S.-Israel Bi-National Science Foundation Grant # 680.