A remark on homology localization (Q1392511)

A classical result of \textit{A. K. Bousfield} [Topology 14, 133-150 (1975; Zbl 0309.55013)] asserts that, given a homology theory \(h\) on \(hoCW\), the homotopy category of CW-spaces, there is \(h\)-localization \(X\to X_h\) on \(hoCW\). This process is functorial and idempotent. It is characterized by the property that it turns precisely those maps \(f:X\to Y\) into homotopy equivalences for which \(h(f)\) is an isomorphism. The author generalizes this result: Given \(h\) as above and an integer \(n\), there exists a localizing functor on \(hoCW\) which turns precisely those maps \(f:X\to Y\) into homotopy equivalences for which \(h_k(f)\), \(k<n\), is an isomorphism.