# 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 $\mathbb{Q}={\displaystyle \bigcup _{n\in \mathbb{N}}}\{{r}_{n}\}$ and, for every $n\in \mathbb{N}$, $\mathrm{int}\overline{\{{r}_{n}\}}=\mathrm{int}\{{r}_{n}\}=\mathrm{\varnothing}$.

Title | example of a meager set |
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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 |