A whitehead theorem for long towers of spaces

We show that one can construct the universal R-homology isomorphism K →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 smallest s containing K(A, n)'s and closed under homotopy inverse limit.