We dont have to do this now (first lets deal with CW complex and weakly contractible etc), but this is a very common variant of a CW complex. I dont think we can encode it currently (unlike Finite CW complex).
A CW complex is finite dimensional iff the skeleta stabilise. Notably its nontrivial to prove this is preserved by homeomorphisms/well-defined.a
We dont have to do this now (first lets deal with CW complex and weakly contractible etc), but this is a very common variant of a CW complex. I dont think we can encode it currently (unlike Finite CW complex).
A CW complex is finite dimensional iff the skeleta stabilise. Notably its nontrivial to prove this is preserved by homeomorphisms/well-defined.a