8 problems.
- Compact subsets of Hausdorff spaces are closed
- Union of connected subspaces sharing a point is connected
- Connected double covers of \(S^1\vee S^1\) and the index-\(2\) subgroups of \(F_2\)
- Every continuous map \(\RP^2\to S^1\times S^1\) is null-homotopic
- van Kampen’s theorem and \(\pi_1\) of two tori glued along a circle
- Cell structure and homology of the torus \(S^1\times S^1\)
- Homology of \(S^2\) glued to a torus along an equatorial circle
- Genus of a closed orientable surface admitting a fixed-point-free map homotopic to the identity