\begin{definition}[Definition:Discrete Subgroup/Real Numbers]
Let $G$ be a subgroup of the additive group of real numbers.
Then $G$ is '''discrete''' {{iff}}:
:$\forall g \in G: \exists \epsilon \in \R_{>0}: \openint {g - \epsilon} {g + \epsilon} \cap G = \set g$
That is, there exists a neighborhood of $g$ which contains no other elements of $G$.
Category:Definitions/Subgroups
Category:Definitions/Topological Groups
Category:Definitions/Real Numbers
\end{definition}