9 problems.
- Core point-set definitions and four separation/product theorems
- Connected metric spaces with more than one point are uncountable — Problem 2; repeated exactly as the canonical connected-metric-space exercise
- Zorn’s lemma and existence of maximal ideals
- Maximal ideals of rings of continuous functions on compact Hausdorff spaces
- Singular homology, a prescribed CW homology example, and Mayer–Vietoris
- The simply connected case of van Kampen and the full theorem
- A Hausdorff space with a clopen basis is totally disconnected
- Boundary inclusion for a punctured genus-\(2\) surface and obstruction to a retraction
- Fundamental group of a sphere with a diameter adjoined via its simply connected cover