9 problems.
- Nested nonempty closed subsets of a compact space have nonempty intersection
- \(\overline{U}\setminus U\) is nowhere dense for \(U\) open
- The union of connected sets is connected if one meets the closure of the other
- The distance between compact sets in a metric space is attained
- \(\RR\) and \(\RR^2\) are not homeomorphic
- Maps \(X\to S^1\) are nullhomotopic when \(\pi_1(X)\) is finite
- Fundamental group of \(\RR^3\) minus the three coordinate axes
- No retraction from \(S^2\) onto an equatorial circle
- Deck transformations sending \(y_0\) to \(y_1\) iff \(p_*(\pi_1(\widetilde{X},y_0))=p_*(\pi_1(\widetilde{X},y_1))\)