Cellular Approximation: Homotopy and CW Complexes

This lecture focuses on proving the cellular approximation theorem, which states that any map between CW complexes is homotopic to a cellular map. The instructor discusses the process of simplifying maps cell by cell and the historical background of Whitehead's contributions to CW complexes. The lecture delves into the logical construction of the course, the proof by induction, and the construction of homotopies. The implications of the theorem on homotopy groups of spheres and connectivity for pairs are also explored, providing a foundational understanding of homotopy theory.