This sheet is based on Lectures 19 and 20.

• Problem 1 show that strong deformation retractions really are stronger than normal deformation retractions.
• Problem 2 is just easy.
• Problems 3 and 4 introduce the Euler characteristic.
• Problem 5 asks you to come up[1] with an explicit isomorphism $H_n(X) \cong H_n(X, \mathcal{F})$.
• Problem 6 gives a categorical interpretation of cell-like filtrations.

As usual, feel free to ask questions if you are stuck! 😀

1. Actually I thought this was a bit hard, so I pretty much just told you the answer. But you still need to verify what I claim works. ↩︎