 CW approximation, being a weak homotopy equivalence, induces isomorphisms on homology and cohomology groups of "X".Thus one often can use CW approximation to reduce a general statement to a simpler version that only concerns CW complexes.CW approximation is constructed inducting on skeleta formula_28 of formula_29, so that the maps formula_30 are isomorphic for formula_31 and are onto for formula_32 (for any basepoint).