9 problems.
- The metric topology of a smaller metric is coarser
- Closed subsets of limit-point compact spaces are limit-point compact
- Borsuk–Ulam theorem for maps \(S^1\to\RR\)
- A strictly finer topology on a compact Hausdorff space is Hausdorff but not compact
- Local connectedness via open components, and preservation under quotient maps
- Cell structure and fundamental group of two tori glued along a meridian and a longitude
- The pullback of a covering map is a covering map
- Simplicial homology of three disks with identified boundaries
- Singular homology of the \(2\)-torus via Mayer–Vietoris