# theorem about continuous convergence

Let $(X,d)$ and $(Y,\rho )$ be metric spaces, and let ${f}_{n}:X\u27f6Y$ be a sequence of continuous functions. Then ${f}_{n}$ converges continuously to $f$ if and only if ${f}_{n}$ converges uniformly to $f$ on every compact subset of $X$.

Title | theorem about continuous convergence |
---|---|

Canonical name | TheoremAboutContinuousConvergence |

Date of creation | 2013-03-22 14:05:00 |

Last modified on | 2013-03-22 14:05:00 |

Owner | gumau (3545) |

Last modified by | gumau (3545) |

Numerical id | 5 |

Author | gumau (3545) |

Entry type | Theorem |

Classification | msc 54A20 |