# Problem Sheet D

This sheet is based on Lectures 7 and 8.

- Problem 1 asks to prove some fun facts about (free) abelian groups. Yay, group theory! π
- Problem 2 asks you to show that all simplices are homeomorphic to balls.
*Hint:*First prove it for the standard $n$-simplex $ \Delta^n$. Then show any two $n$-simplices are homeomorphic via an affine map. - Problem 3 has a fancy name: this is the
*dimension axiom*. It won't be until the end of the course when we cover the*Eilenberg-Steenrod axioms* - Problem 4 relates the homology of a space to that of its path components. Note this is different

This is another nice and easy sheet. π

π€ Feel free to ask a question if you are stuck! π€

Comments and questions?