## When Are Discrete Subgroups Closed?

Let $ H\subseteq G$ be a subgroup of a topological group $ G$ (henceforth abbreviated "group"). If the induced topology on $ H$ is discrete, then we say that $ H$ is a discrete subgroup of $ G$. A commonplace example is the subgroup $ \mathbb{Z}\subseteq \mathbb{R}$: the integers are normal subgroup of the real […]