8 problems.
- Disjoint open sets in an extremally disconnected space have disjoint closures
- A connected locally path-connected space is path-connected
- If \(f\) is a compact-to-Hausdorff continuous surjection and \(g\circ f\) is continuous, then \(g\) is continuous
- The product of two locally compact spaces is locally compact
- A simply-connected open cover of \(T^2\) has an empty or disconnected noninitial consecutive intersection
- A covering space restricts to a subspace, with \(\ker\iota_*\subseteq\operatorname{im}q_*\)
- A genus-2 surface is not a retract of the region it bounds
- Euler characteristic and homology of \((\Delta^5)^{(2)}\)