# Dini’s theorem

If a monotonically increasing net $\{{f}_{n}\}$ of continuous^{} real-valued functions on a topological space^{} $(X,\tau )$ converges^{} pointwise^{} to a continuous function $f$, then the net converges to $f$ uniformly on compacts^{}.

Title | Dini’s theorem |
---|---|

Canonical name | DinisTheorem |

Date of creation | 2013-03-22 12:20:32 |

Last modified on | 2013-03-22 12:20:32 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 4 |

Author | drini (3) |

Entry type | Theorem |

Classification | msc 54A20 |

Related topic | TopologicalSpace |

Related topic | Compact |