# connected set in a topological space

Let $Y$ be a topological space^{} and $X\subseteq Y$ be given the subspace topology. We say that $X$ is connected iff we cannot find nonempty open sets $U,V\subseteq X$ such that $U\cap V=\mathrm{\varnothing}$ and $U\cup V=X$.

Title | connected set in a topological space |
---|---|

Canonical name | ConnectedSetInATopologicalSpace |

Date of creation | 2013-03-22 13:59:51 |

Last modified on | 2013-03-22 13:59:51 |

Owner | ack (3732) |

Last modified by | ack (3732) |

Numerical id | 6 |

Author | ack (3732) |

Entry type | Definition |

Classification | msc 54D05 |