example of a meager set

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

Title	example of a meager set
Canonical name	ExampleOfAMeagerSet
Date of creation	2013-03-22 17:07:08
Last modified on	2013-03-22 17:07:08
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	4
Author	Wkbj79 (1863)
Entry type	Example
Classification	msc 54E52
Related topic	ExamplesOfNowhereDenseSets