examples of nowhere dense sets

Note that $\mathbb{Z}$ is nowhere dense in $ℝ$ under the usual topology: $\mathrm{int}\overline{\mathbb{Z}}=\mathrm{int}\mathbb{Z}=\mathrm{\varnothing }$. 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 $ℝ$ under the usual topology, since $\mathbb{Q}={\displaystyle \bigcup _{n\in \mathbb{Z}\text{ and }n>0}}\frac{1}{n}\mathbb{Z}$.

Title	examples of nowhere dense sets
Canonical name	ExamplesOfNowhereDenseSets
Date of creation	2013-03-22 17:07:05
Last modified on	2013-03-22 17:07:05
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	4
Author	Wkbj79 (1863)
Entry type	Example
Classification	msc 54A99
Related topic	ExampleOfAMeagerSet