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Original solutions to past examinations of the topology and groups course of the University of Oxford.

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 $f(x)$.