19 problems.
- Compact subsets of metric spaces are closed and bounded
- Complete subspaces of complete metric spaces
- The closure is contained in every closed superset
- Continuity of the distance to a subset
- Closed subsets of compact spaces and compact subsets of Hausdorff spaces
- Closed-map and open-map criteria for identification maps
- The Hausdorff criterion for a product of two spaces
- The open unit interval is not compact
- Connectedness of the real line
- The rational-translation quotient of R has the indiscrete topology
- Connected components in a locally connected space are open
- Infinite sets and limit points in compact spaces
- Collapsing the boundary of a Möbius band gives \(\mathbb{RP}^2\)
- Non-surjective maps into a sphere are homotopic
- Associativity of the product of loop homotopy classes
- Deformation retracts and the fundamental group of \(\mathbb R^3\) minus a circle
- The surface with polygonal symbol \(xy^{-1}x^{-1}zwz^{-1}\nu yw^{-1}\nu^{-1}\), and classification of closed surfaces by even-sided polygons
- \(n\)-sheeted coverings of \(S^1\) and subgroup index
- Euler characteristic of the n-sphere from a standard triangulation