# subspace topology

Let $X$ be a topological space^{}, and let $Y\subset X$ be a subset. The subspace topology on $Y$ is the topology whose open sets are those subsets of $Y$ which equal $U\cap Y$ for some open set $U\subset X$.

In this context, the topological space $Y$ obtained by taking the subspace topology is called a topological subspace, or simply subspace^{}, of $X$.

Title | subspace topology |
---|---|

Canonical name | SubspaceTopology |

Date of creation | 2013-03-22 11:53:22 |

Last modified on | 2013-03-22 11:53:22 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 8 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 54B05 |

Classification | msc 15A66 |

Classification | msc 11E88 |

Synonym | relative topology |

Defines | topological subspace |

Defines | subspace |