 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-1-course-of-the-university-of-oxford/2011/4/a/solution

The integers are unbounded in the complex plane, so the Heine-Borel theorem shows they are not compact. They are also not connected:

{0}

and

Z ∖ {0}

are disjoint nonempty relatively open sets covering

Z

. Each integer is isolated, so the induced subspace topology is discrete.

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