# isolated

Let $X$ be a topological space^{}, let $S\subset X$, and let $x\in S$. The point $x$ is said to be an *isolated* point of $S$ if there exists an open set $U\subset X$ such that $U\cap S=\{x\}$.

The set $S$ is *isolated* or *discrete* if every point in $S$ is an isolated point.

Title | isolated |
---|---|

Canonical name | Isolated |

Date of creation | 2013-03-22 12:05:59 |

Last modified on | 2013-03-22 12:05:59 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 8 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 54A05 |

Synonym | discrete set |

Defines | isolated set |

Defines | isolated point |