In the appendix of Allen Hatcher's book "Algebraic Topology", a CW complex is defined to be a space iteratively constructed by attaching n-cells $n$-cells onto an (n-1) $(n-1)$ skeleton. There is a more general notion where a space can be built iteratively by attaching cells, however we pose no restriction on the order of attachment. For instance the endpoints of a 1-cell $1$-cell could be glued onto the interior of a 2-cell. $2$-cell. This notion is discussed in Chris Schommer-Pries' answer to another MO question:
Does this kind of complex have a name?
