 Solution

ID: past-exam-of-the-metric-spaces-and-complex-analysis-course-of-the-university-of-oxford/2015/1/c/iii/solution

The unit circle is the inverse image of the closed set

{1}

(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 compactness.

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