# ${G}_{\delta}$ set

A ${G}_{\delta}$ set is a set which can be expressed as the intersection^{} of a countable^{} collection^{} of open sets.

The complement of a ${G}_{\delta}$ set is an ${F}_{\sigma}$ set (http://planetmath.org/F_sigmaSet).

For example, the closed interval^{} $[-1,+1]\in \mathbb{R}$ is a ${G}_{\delta}$ set because

$$[-1,+1]=\bigcap _{n=1}^{\mathrm{\infty}}(-\frac{1}{n}-1,\frac{1}{n}+1)$$ |

Title | ${G}_{\delta}$ set |
---|---|

Canonical name | GdeltaSet |

Date of creation | 2013-03-22 14:38:02 |

Last modified on | 2013-03-22 14:38:02 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 7 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 54A05 |

Related topic | F_sigmaSet |

Related topic | PavedSet |

Related topic | PavedSpace |