Hatcher, Algebraic Topology, Chapter 2, Section 1
22. Prove by induction on dimension the following facts about the homology of a finite-dimensional CW complex , using the observation that is a wedge sum of -spheres:
(a) If has dimension then for and is free.
(b) is free with basis in bijective correspondence with the -cells if there are no cells of dimension or .
(c) If has -cells, then is generated by at most elements.