CW-complexes and relative cell complexes

Remark 2.3.2. While the definition involves ordinals to handle potentially transfinite constructions, for many common examples the process involves only a finite or countable number of steps. For example, every cell complex is homotopy equivalent to a CW-complex, which is a cell complex where \(\lambda = \omega \) is the set of natural numbers, and where the dimensions of the cells attached at step \(n \in \omega \) is \(n\).