# generic point

Let $X$ be a topological space^{} and suppose that $x\in X$. If for all $y\in X\backslash \{x\}$ we have $x\notin \overline{\{y\}}$ then we say that $x$ is a *generic point*. Equivalently, $x$ is generic iff it is not a specialization point of any point in $X$, other than $x$ itself.

Title | generic point |
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Canonical name | GenericPoint |

Date of creation | 2013-03-22 16:22:28 |

Last modified on | 2013-03-22 16:22:28 |

Owner | jocaps (12118) |

Last modified by | jocaps (12118) |

Numerical id | 8 |

Author | jocaps (12118) |

Entry type | Definition |

Classification | msc 54A05 |

Defines | generic point |

Defines | generic |