\b[False.] In the additive <topological group> $\mathbb R$, the <subgroup> $\mathbb Z$ is closed: every noninteger has a sufficiently small interval disjoint from it. It is not open, because no neighbourhood of an integer consists only of integers. Thus a <closed subgroup> need not be an <open subgroup>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 9 / 1 / a / Solution

 Solution (source code)