# connected component

Two points $x,y$ in a topological space^{} $X$ are said to be in the same connected component^{} if there exists a subspace^{} of $X$ containing $x$ and $y$ which is connected. This relation^{} is an equivalence relation^{}, and the equivalence classes^{} of $X$ under this relation are called the connected components of $X$.

Title | connected component |
---|---|

Canonical name | ConnectedComponent |

Date of creation | 2013-03-22 12:00:21 |

Last modified on | 2013-03-22 12:00:21 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 6 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 54D05 |