9 problems.
- The product of two compact spaces is compact
- An example of a connected space that is not path-connected
- Euler characteristic of a compact surface with \(k\) boundary components is at most \(2-k\)
- Coverings of simply connected spaces and the missing path-connectedness hypothesis
- Free subgroups of \(F_2\) of every finite or countable rank, via covering spaces
- Fundamental group and homology of a torus with \(2\)-cells attached along a meridian and a longitude
- Homology of \(S^n\) via Mayer–Vietoris
- Cellular homology of the quotient \(\RP^n/\RP^m\)
- Fixed-point-free maps homotopic to the identity on orientable surfaces, and the missing closedness hypothesis