Note that $\mathbb{Z}$ is nowhere dense in $\mathbb{R}$ under the usual topology: $\operatorname{int} \overline{\mathbb{Z}}=\operatorname{int} \mathbb{Z}=\emptyset$ Similarly, $\frac{1}{n} \mathbb{Z}$ is nowhere dense for every $n \in \mathbb{Z}$ with $n>0$

This result provides an alternative way to prove that $\mathbb{Q}$ is meager in $\mathbb{R}$ under the usual topology, since $\displaystyle \mathbb{Q}=\bigcup_{n \in \mathbb{Z} { and } n>0} {\frac{1}{n}} \mathbb{Z}$