# closed graph theorem

A linear mapping between two Banach spaces^{} $X$ and $Y$ is continuous^{} if and only if its graph (http://planetmath.org/Graph2) is a closed subset of $X\times Y$ (with the product topology).

Title | closed graph theorem |
---|---|

Canonical name | ClosedGraphTheorem |

Date of creation | 2013-03-22 13:13:56 |

Last modified on | 2013-03-22 13:13:56 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 8 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 46A30 |

Related topic | OpenMappingTheorem |

Related topic | Graph2 |