 Solution

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

The open unit disk is bounded but not closed:

(1 - 1/ n, 0)

lies in it for

n \geq 2

and converges to the omitted point

(1, 0)

. By the Heine-Borel theorem, it is not compact.

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