 2023

Solutions to all three questions of the topology and groups course of the University of Oxford Part B examination, sat on 31 May 2023. Source: original released PDF, bundle pages 221–223; paper pages 1–3. The Mathematics and Statistics version is labelled B3.4. All eighteen parts are treated below. Question 3(a)(iii), as printed, needs an additional hypothesis such as local path connectedness; its solution includes both the intended argument and a counterexample to the unrestricted assertion.

Throughout Question 1, $I=[0,1]$ has its usual topology, and the mapping cylinder uses the paper's convention that $(x,1)$ is attached to $f(x)$.