8 problems.
- Covering maps inject on \(\pi_1\), and a \(\pi_1\)-isomorphism implies a homeomorphism
- \(\pi_1\) of a torus with three distinct points identified
- Possible homology of \(\RP^2\) with a \(2\)-cell attached
- \(\RP^2\vee S^1\) is not homotopy equivalent to a compact surface
- Lefschetz fixed-point theorem for finite simplicial complexes, and the case \(X=S^n\)
- Compact subsets of Hausdorff spaces are closed
- Discrete spaces are totally disconnected, but not conversely
- Open sets in a second-countable regular space as countable unions of closed sets, with a continuous \(f:X\to[0,1]\) positive on \(U\)