In this paper we introduce a new tool in algebraic topology which is called
(analogous terminology of J.H.C. Whitehead in [1] ) .
By studying effect of this complex on the spectral sequences , we obtained some
results , such as ;
1- Any complex is an
2- Let are two cw-complexes , if , then
.
3- If is , then
.
4- Let be a cw-complex , if is a , then is a
, and the converse is not true .