# fibre map

A fibre map is a map of topological spaces^{} $f:E\to B$, for which there exists a space $F$, such that any point of $B$ is contained in some neighbourhood $U$ satisfying the following: on ${f}^{-1}U$, $f$ restricts to the natural projection $F\times U\to U$, via some homeomorphic identification of ${f}^{-1}U$ with $F\times U$.

One class of examples are covering maps. Another example is the map $S{O}_{3}\to {S}^{2}$ sending a rotation to the point it sends the “North Pole^{}” to.

Title | fibre map |

Canonical name | FibreMap |

Date of creation | 2013-03-22 14:32:27 |

Last modified on | 2013-03-22 14:32:27 |

Owner | whm22 (2009) |

Last modified by | whm22 (2009) |

Numerical id | 11 |

Author | whm22 (2009) |

Entry type | Definition |

Classification | msc 55R10 |

Synonym | fiber map |

Related topic | FibreBundle |

Related topic | LocallyTrivialBundle |

Related topic | LongExactSequenceLocallyTrivialBundle |

Related topic | Fibration2 |

Related topic | HomotopyLiftingProperty |

Defines | fibre map |