# normal

A topological space^{} $X$ is said to be *normal* if $X$ is ${T}_{1}$ (i.e. singletons are closed), and for all disjoint closed sets $D,F\subseteq X$ there exist disjoint open sets $U$ and $V$ such that $C\subseteq U$ and $D\subseteq V$ (i.e, $X$ is also ${T}_{4}$).

Some authors do not require the ${T}_{1}$ axiom as part of this definition.

Title | normal |

Canonical name | Normal |

Date of creation | 2013-03-22 12:12:39 |

Last modified on | 2013-03-22 12:12:39 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 14 |

Author | Koro (127) |

Entry type | Definition |

Classification | msc 54D15 |

Synonym | normality^{} |

Synonym | normal |

Related topic | SeparationAxioms |

Related topic | Tychonoff^{} |

Related topic | Hausdorff^{} |

Related topic | CompletelyNormal |

Related topic | T2Space |

Related topic | AConnectedNormalSpaceWithMoreThanOnePointIsUncountable2 |

Related topic | AConnectedNormalSpaceWithMoreThanOnePointIsUncountable |

Related topic | ApplicationsOfUrysohnsLemmaToLocallyCompactHausdorffSpaces |