# open mapping theorem

There are two important theorems having this .

$\bullet $ In the context of functions of a complex variable:

Theorem. Every non-constant analytic function^{} on a region is an open mapping.

$\bullet $ In the context of functional analysis^{}:

Theorem. Every surjective continuous linear mapping between two Banach spaces^{} is an open mapping.

Title | open mapping theorem^{} |
---|---|

Canonical name | OpenMappingTheorem |

Date of creation | 2013-03-22 13:12:41 |

Last modified on | 2013-03-22 13:12:41 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 14 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 30A99 |

Classification | msc 46A30 |

Related topic | ClosedGraphTheorem |