# locally connected

A topological space^{} $X$ is locally connected at a point $x\in X$ if every neighborhood^{} $U$ of $x$ contains a connected^{} neighborhood $V$ of $x$. The space $X$ is locally connected if it is locally connected at every point $x\in X$.

A topological space $X$ is locally path connected at a point $x\in X$ if every neighborhood $U$ of $x$ contains a path connected neighborhood $V$ of $x$. The space $X$ is locally path connected if it is locally path connected at every point $x\in X$.

Title | locally connected |
---|---|

Canonical name | LocallyConnected |

Date of creation | 2013-03-22 12:38:48 |

Last modified on | 2013-03-22 12:38:48 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 5 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 54D05 |

Related topic | ConnectedSet |

Related topic | ConnectedSpace |

Related topic | PathConnected |

Related topic | SemilocallySimplyConnected |

Defines | locally path connected |