# topological sum

Given two topological spaces^{} $X$ and $Y$, their *topological sum* is defined
to be the set $X\coprod Y$ (see the entry *disjoint union ^{}*) equipped with
the finest topology such that the inclusion maps

^{}from $X$ and $Y$ into $X\coprod Y$ are continuous

^{}. A basis for this topology consists of the union of the set of open subsets of $X$ and the set of open subsets of $Y$.

Title | topological sum |
---|---|

Canonical name | TopologicalSum |

Date of creation | 2013-03-22 14:41:29 |

Last modified on | 2013-03-22 14:41:29 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 7 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 54A99 |

Synonym | coproduct^{} in the category of topological spaces |

Synonym | topological disjoint union |