# pointwise convergence

Let $X$ be any set, and let $Y$ be a topological space^{}.
A sequence^{} ${f}_{1},{f}_{2},\mathrm{\dots}$ of functions mapping $X$ to $Y$ is said to be *pointwise convergent ^{}* (or simply convergent) to another function $f$, if the sequence ${f}_{n}(x)$ converges to $f(x)$ for each $x$ in $X$. This is usually denoted by ${f}_{n}\to f$.

Title | pointwise convergence |
---|---|

Canonical name | PointwiseConvergence |

Date of creation | 2013-03-22 13:15:28 |

Last modified on | 2013-03-22 13:15:28 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 4 |

Author | Koro (127) |

Entry type | Definition |

Classification | msc 40A30 |

Defines | pointwise |