3 Texified, since it was on the front-page anyway

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:

http://mathoverflow.net/questions/74863/what-does-actually-being-a-cw-complex-provide-in-algebraic-topology/74904#74904

Does this kind of complex have a name?

2 tag typo
1

# The definition of a CW complex and related notions

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 onto an (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 could be glued onto the interior of a 2-cell. This notion is discussed in Chris Schommer-Pries' answer to another MO question:

http://mathoverflow.net/questions/74863/what-does-actually-being-a-cw-complex-provide-in-algebraic-topology/74904#74904

Does this kind of complex have a name?