# example of a meager set

Note that $\mathbb{Q}$ is meager in $\mathbb{R}$ under the usual topology. Let $\{r_{n}\}_{n\in\mathbb{N}}$ be an enumeration of $\mathbb{Q}$. Then $\displaystyle\mathbb{Q}=\bigcup_{n\in\mathbb{N}}\{r_{n}\}$ and, for every $n\in\mathbb{N}$, $\operatorname{int}\overline{\{r_{n}\}}=\operatorname{int}\{r_{n}\}=\emptyset$.

Title example of a meager set ExampleOfAMeagerSet 2013-03-22 17:07:08 2013-03-22 17:07:08 Wkbj79 (1863) Wkbj79 (1863) 4 Wkbj79 (1863) Example msc 54E52 ExamplesOfNowhereDenseSets