# homeomorphism

A *homeomorphism* $f$ of topological spaces^{} is a continuous^{}, bijective^{} map such that ${f}^{-1}$ is also continuous. We also say that two spaces are *homeomorphic* if such a map exists.

If two topological spaces are homeomorphic, they are topologically equivalent — using the techniques of topology, there is no way of distinguishing one space from the other.

An *autohomeomorphism* (also known as a *self-homeomorphism*) is a
homeomorphism from a topological space to itself.

Title | homeomorphism |

Canonical name | Homeomorphism |

Date of creation | 2013-03-22 11:59:35 |

Last modified on | 2013-03-22 11:59:35 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 16 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 54C05 |

Synonym | topological equivalence |

Synonym | topologically equivalent |

Related topic | Homeotopy |

Related topic | CrosscapSlide |

Related topic | AlexanderTrick |

Related topic | GroupoidCategory |

Defines | homeomorphic |

Defines | autohomeomorphism |

Defines | auto-homeomorphism |

Defines | self-homeomorphism |