# Tag Archives: discrete subgroups

## 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 […]