Postnikov system
In homotopy theory, a branch of algebraic topology, a Postnikov system (or Postnikov tower) is a way of decomposing a topological space by filtering its homotopy type. For a space X {\displaystyle X} , this is a list of spaces { X n } n ≥ 0 {\displaystyle \{X_{n}\}_{n\geq 0}} where π k ( X n ) = { π k ( X ) for k ≤ n 0 for k > n {\displaystyle \pi _{k}(X_{n})={\begin{cases}\pi _{k}(X)&{\text{ for }}k\leq n\\0&{\text{ for }}k>n\end{cases}}} and a series of maps ϕ n : X n → X n − 1 {\displaystyle \phi _{n}:X_{n}\to X_{n-1}} that are fibrations with Eilenberg-MacLane spaces K ( π n ( X ) , n ) {\displaystyle K(\pi _{n}(X),n)} as fibers.