The <unit circle> is the inverse image of the <closed set> $\{1\}$ under the <continuous map> $(x,y)\mapsto x^2+y^2$, so it is <closed>. It is also <bounded>, since every point has <Euclidean norm> one. The <Heine-Borel theorem> gives \b[<compactness>].

Solution

Past exam of the metric spaces and complex analysis course of the University of Oxford / 2015 / 1 / c / iii / Solution

 Solution (source code)