{c}

The <integers> are unbounded in the <complex plane>, so the <Heine-Borel theorem> shows they are \b[not compact]. They are also \b[not connected]: $\{0\}$ and $\mathbb Z\setminus\{0\}$ are disjoint nonempty relatively <open sets> covering $\mathbb Z$. Each integer is isolated, so the induced <subspace topology> is discrete.

Solution

Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2011 / 4 / a / Solution

 Solution (source code)