 In detail, assume formula_1 to be the total space of a Serre fibration with fibre formula_12 and base space formula_13.The filtration of formula_13 by its formula_15-skeletons formula_16 gives rise to a filtration of formula_1.There is a corresponding spectral sequence with formula_5 term

and abutting to the associated graded ring of the filtered ring

This is the Atiyah–Hirzebruch spectral sequence in the case where the fibre formula_12 is a point.