1.4 Introduction to Algebraic Topology. First Theorem

Two Theorems about CW-comples are fundamental. The first one we prove in this lecture. Both the Theorems use the Homotopy Extension Property of CW-complexes. The Theorem we consider states that modding out a contractible subcomplex in a CW-complex will result in an homotopy equivalence. Notice that the contracting homotopy MUST take values in the subspace and outside.