The last few posts have all been of relatively long length and have all taken some time to construct and write. I initially also wanted to produce shorter posts just discussing an example or a calculation etc, and today I tried to do just that, but failed. The post became somewhat longer than intended, but it is really informal and intuitive, so its fine in my opinion.
In a previous post we discussed both weak homotopy equivalences and regular homotopy equivalences, and we have also encountered the Whitehead theorem, which says that any weak homotopy equivalence between CW-complexes is in fact a regular homotopy equivalence....