# quasicomponent

Let $X$ be a topological space^{}. Define a relation^{} $\sim $ on $X$ as follows: $x\sim y$ if there is no partition of $X$ into disjoint open sets $U$ and $V$ such that $U\cup V=X$, $x\in U$ and $y\in V$.

This is an equivalence relation^{} on $X$. The equivalence classes^{} are called the *quasicomponents* of $X$.

Title | quasicomponent |
---|---|

Canonical name | Quasicomponent |

Date of creation | 2013-03-22 12:23:49 |

Last modified on | 2013-03-22 12:23:49 |

Owner | Evandar (27) |

Last modified by | Evandar (27) |

Numerical id | 4 |

Author | Evandar (27) |

Entry type | Definition |

Classification | msc 54D05 |

Synonym | quasi-component |

Related topic | ConnectedSpace |

Related topic | PathConnected |

Related topic | ConnectedComponent |

Related topic | PathComponent |