# open mapping

Let $X$ and $Y$ be two topological spaces^{}. A function $f:X\to Y$ is
said to be open if $f(U)$ is open for each open subset $U$ of $X$.

Accordingly, if $f(C)$ is closed for each closed subset $C$ of $X$, we say that $f$ is closed.

Title | open mapping |
---|---|

Canonical name | OpenMapping |

Date of creation | 2013-03-22 13:12:45 |

Last modified on | 2013-03-22 13:12:45 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 4 |

Author | Koro (127) |

Entry type | Definition |

Classification | msc 54C10 |

Synonym | open function |

Defines | closed function |

Defines | closed mapping |