# continuous convergence

Let $(X,d)$ and $(Y,\rho )$ be metric spaces, and let ${f}_{n}:X\u27f6Y$ be a sequence of functions. We say that ${f}_{n}$ converges continuously to $f$ at $x$ if ${f}_{n}({x}_{n})\u27f6f(x)$ for every sequence ${({x}_{n})}_{n}\subset X$ such that ${x}_{n}\u27f6x\in X$. We say that ${f}_{n}$ *converges continuously* to $f$ if it does for every $x\in X$.

Title | continuous convergence |
---|---|

Canonical name | ContinuousConvergence |

Date of creation | 2013-03-22 14:04:58 |

Last modified on | 2013-03-22 14:04:58 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 7 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 54A20 |

Synonym | converges continuously |