1.5 Introduction to Algebraic Topology. Second Theorem on CW complexes.

The second Theorem on CW complexes implies, in particular, that, if we take a topological space Y and attach to it a cell first by an attaching map f and then by another map g, the resulting spaces have the same homotopy type, provided f and g are homotopic. Along with the first Theorem on CW complexes discussed in Lecture 1.4, this result provide a key tool to deform a CW complex in the hope of understanding better its homotopy type.