Homotopy Type of CW Complexes

Abstract

In this chapter we will study conditions on a space that will cause it to have the homotopy type of a CW complex and prove a theorem of J. H. C. Whitehead which gives a criterion that a map between two such spaces be a homotopy equivalence. We note in passing that there is a method using elaborate algebraic techniques (the analysis of Postnikov systems) for determining, in principle, whether two such spaces have the same homotopy type, but this is beyond the scope of this book.